RD Sharma Solutions for Class 12 Maths Chapter 11 Differentiation

RD Sharma books offer several questions for practice at the end of each chapter. RD Sharma solutions provided here are easily readable and sketched in such a way to help students clear all their doubts that they might face, while answering the given problems in exercises. These solutions are prepared by BYJU’S experts in Maths. The PDF of RD Sharma Solutions for Class 12 Maths Chapter 11 Differentiation is provided here. Students can refer and download Chapter 11 Differentiation from the given links. These solutions facilitate students to create good knowledge about basic concepts of Mathematics. This chapter is based on the differentiation of given function. Some of the essential topics of this chapter are listed below.

  • Recapitulation of the product rule, quotient rule and differentiation of a constant with an illustration.
  • Differentiation of inverse trigonometric functions from first principles.
  • Differentiation of a function of a function.
  • Differentiation of inverse trigonometric functions by the chain rule.
  • Differentiation by using trigonometrical substitutions.
  • Differentiation of implicit functions.
  • Logarithmic differentiation.
  • Differentiation of infinite series.
  • Differentiation of parametric functions.
  • Differentiation of a function with respect to another function.
  • Differentiation of determinants.

RD Sharma Solutions For Class 12 Maths Chapter 11 Differentiation:-Download PDF Here

RD Sharma Class 12 Maths Solutions Chapter 11 Differentiation
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Access answers to Maths RD Sharma Solutions For Class 12 Chapter 11 – Differentiation

Exercise 11.1 Page No: 11.17

Differentiate the following functions from the first principles:

1. e-x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 1

2. e3x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 2

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 3

3. eax + b

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 4

4. ecos x

Solution:

We have to find the derivative of ecos x with the first principle method,

So, let f (x) = ecos x

By using the first principle formula, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 5

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 6

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 7

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 8

Exercise 11.2 Page No: 11.37

Differentiate the following functions with respect to x:

1. Sin (3x + 5)

Solution:

Given Sin (3x + 5)

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 9

2. tan2 x

Solution:

Given tan2 x

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 10

3. tan (xo + 45o)

Solution:

Let y = tan (x° + 45°)

First, we will convert the angle from degrees to radians.

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 11

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 12

4. Sin (log x)

Solution:

Given sin (log x)

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 13

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 14

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 16

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 17

6. etan x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 18

7. Sin2 (2x + 1)

Solution:

Let y = sin2 (2x + 1)

On differentiating y with respect to x, we get

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 19

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 20

8. log7 (2x – 3)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 21

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 22

9. tan 5xo

Solution:

Let y = tan (5x°)

First, we will convert the angle from degrees to radians. We have

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 23

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 25

Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 28

12. logx 3

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 29
RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 30

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 32

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 34

Solution:

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Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 42

Solution:

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Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 54

18. (log sin x)2

Solution:

Let y = (log sin x)2

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 55

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 56

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 57

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 58

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 61

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 63

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 64

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 65

21. e3x cos 2x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 66

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 67

22. Sin (log sin x)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 68

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 69

23. etan 3x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 70

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 71

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 72

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 73

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 75

Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 80

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 81

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 84

27. tan (esin x)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 85

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 86

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 87

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 88

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 90

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Solution:

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30. log (cosec x – cot x)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 95

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Solution:

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Solution:

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33. tan-1 (ex)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 107

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 108

Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 110

35. sin (2 sin-1 x)

Solution:

Let y = sin (2sin–1x)

On differentiating y with respect to x, we get

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 111

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 113

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 114

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Solution:

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 119

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 120

Exercise 11.3 Page No: 11.62

Differentiate the following functions with respect to x:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 121

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 122

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 123

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 124

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 125

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 127

Solution:

Let,
RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 128

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 129

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 130

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 131

Solution:

Let,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 132

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 133

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 134

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 135

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 136

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 138

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 139

7. Sin-1 (2x2 – 1), 0 < x < 1

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 140

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 141

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 142

8. Sin-1 (1 – 2x2), 0 < x < 1

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 143

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 144

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 146

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RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 148

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 149

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 152

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 155

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 158

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 163

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 166

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 171

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 174

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 177

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 178

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 179

Solution:

Let,
RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 180

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 185

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 188

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 191

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Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 194

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Exercise 11.4 Page No: 11.74

Find dy/dx in each of the following:

1. xy = c2

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 196

2. y3 – 3xy2 = x3 + 3x2y

Solution:

Given y3 – 3xy2 = x3 + 3x2y,

Now we have to find dy/dx of given equation, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 197

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 198

3. x2/3 + y2/3 = a2/3

Solution:

Given x2/3 + y2/3 = a2/3,

Now we have to find dy/dx of given equation, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 199

4. 4x + 3y = log (4x – 3y)

Solution:

Given 4x + 3y = log (4x – 3y),

Now we have to find dy/dx of it, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 200

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 201

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 202

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 203

6. x5 + y5 = 5xy

Solution:

Given x5 + y5 = 5xy

Now we have to find dy/dx of given equation, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 204

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 205

7. (x + y)2 = 2axy

Solution:

Given (x + y)2 = 2axy

Now we have to find dy/dx of given equation, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 206

8. (x2 + y2)2 = xy

Solution:

Given (x + y)2 = 2axy

Now we have to find dy/dx of given equation, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 207

9. Tan-1 (x2 + y2)

Solution:

Given tan – 1(x2 + y2) = a,

Now we have to find dy/dx of given function, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 208

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 209

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 210

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 211

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 212

11. Sin xy + cos (x + y) = 1

Solution:

Given Sin x y + cos (x + y) = 1

Now we have to find dy/dx of given function, so by differentiating the equation on both sides with respect to x, we get,

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 213

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 214

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 215

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 216

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 217

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 218

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 219

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 220

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 221

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 222

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 223

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 224

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 225

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 226

Exercise 11.5 Page No: 11.88

Differentiate the following functions with respect to x:

1. x1/x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 227

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 228

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 229

2. xsin x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 230

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 231

3. (1 + cos x)x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 232

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 233

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 234

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 235

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 236

5. (log x)x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 237

6. (log x)cos x

Solution:

Let y = (log x)cos x

Taking log both the sides, we get

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 238

7. (Sin x)cos x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 239

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 240

8. ex log x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 241

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 242

9. (Sin x)log x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 243

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 244

10. 10log sin x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 245

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 246

11. (log x)log x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 247

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 248

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 249

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 250

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 251

13. Sin (xx)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 252

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 253

14. (Sin-1 x)x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 254

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 255

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 256

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 257

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 258

16. (tan x)1/x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 259

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 260

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 261

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 262

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 263

18. (i) (xx) √x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 264

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 265

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 266

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 267

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 268

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 269

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 270

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 271

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 272

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 273

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 274

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 275

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 276

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 277

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 278

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 279

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 280

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 281

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 282

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 283

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 284

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 285

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 286

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 287

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 288

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 289

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 290

18. (vi) esin x + (tan x)x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 291

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 292

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 293

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 294

18. (vii) (cos x)x + (sin x)1/x

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 295

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 296

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 297

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 298

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 299

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 300

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 301

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 301

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 302

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 303

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 304

19. y = ex + 10x + xx

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 305

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 306

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 307

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 308

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 309

20. y = xn + nx + xx + nn

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 310

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 311

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 312

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 313

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 314

Exercise 11.6 Page No: 11.98

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 315

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 316

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 317

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 318

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 319

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 320

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 321

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 322

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 323

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 324

Exercise 11.7 Page No: 11.103

Find dy/dx, when

1. x = at2 and y = 2 at

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 325

2. x = a (θ + sin θ) and y = a (1 – cos θ)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 326

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 327

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 328

3. x = a cos θ and y = b sin θ

Solution:

Given x = a cos θ and y = b sin θ

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 329

4. x = a eθ (sin θ – cos θ), y = a eθ (sin θ + cos θ)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 330

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 331

5. x = b sin2 θ and y = a cos2 θ

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 332

6. x = a (1 – cos θ) and y = a (θ + sin θ) at θ = π/2

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 333

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 334

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 335

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 336

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 337

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 338

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 339

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 340

9. x = a (cos θ + θ sin θ) and y = a (sin θ – θ cos θ)

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 341

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 342

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 343

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 344

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 345

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 346

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 347

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 348

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 349

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 350

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 351

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 352

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 353

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 354

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 355

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 356

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 357

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 358

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 359

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 360

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 361

Exercise 11.8 Page No: 11.112

1. Differentiate x2 with respect to x3.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 362

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 363

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 364

2. Differentiate log (1 +x2) with respect to tan-1 x.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 365

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 366

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 367

3. Differentiate (log x)x with respect to log x.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 368

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 369

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 370

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 371

4. Differentiate sin-1 √ (1-x2) with respect to cos-1x, if

(i) x ∈ (0, 1)

(ii) x ∈ (-1, 0)

Solution:

(i) Given sin-1 √ (1-x2)

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 372

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 373

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 374

(ii) Given sin-1 √ (1-x2)

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 375

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 376

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 377

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 378

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 379

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 380

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 381

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 382

Solution:

(i) Let

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 383

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 384

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 385

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 386

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 387

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 388

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 389

(ii) Let

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 390

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 391

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 392

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 393

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 394

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 395

(iii) Let

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 396

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 397

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 398

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 399

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 400

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 401

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 402

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 403

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 404

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 405

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 406

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 407

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 408

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 409

(i) x ∈ (0, 1/ √2)

(ii) x ∈ (1/√2, 1)

Solution:

(i) Let

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 410

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 411

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 412

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 413

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 414

(ii) Let

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 415

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 416

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 417

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 418

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 419

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 420

8. Differentiate (cos x)sin x with respect to (sin x)cos x.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 421

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 422

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 423

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 424

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 425

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 426

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 427

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 428

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 429

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 430

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 431

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 432

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 433

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 434

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 435

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 436

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 437

RD Sharma Solutions for Class 12 Maths Chapter 11 Diffrentiation Image 438

Also, access RD Sharma Solutions for Class 12 Maths Chapter 11 Differentiation

Exercise 11.1 Solutions

Exercise 11.2 Solutions

Exercise 11.3 Solutions

Exercise 11.4 Solutions

Exercise 11.5 Solutions

Exercise 11.6 Solutions

Exercise 11.7 Solutions

Exercise 11.8 Solutions

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