## RD Sharma Solutions for Class 12 Maths Chapter 11 – Free PDF Download Updated for (2021-22)

**RD Sharma Solutions for Class 12 Maths Chapter 11** â€“ **Differentiation **PDF is provided here for students to score good marks in exams. Students can refer to and download Chapter 11 Differentiation from the given links. These RD Sharma Solutions for Class 12 facilitate students to create good knowledge about basic concepts of CBSE Class 12 Mathematics. This chapter is based on the differentiation of a given function.

RD Sharma books offer several questions for practice at the end of each chapter. **RD Sharma Solutions for Class 12** 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 RD Sharma Solutions are prepared by experts in Maths of BYJUâ€™S.

Some of the primary topics covered in the **RD Sharma Solutions** 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

### 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:**

**2. e ^{3x}**

**Solution:**

**3. e ^{ax + b}**

**Solution:**

**4. e ^{cos x}**

**Solution:**

We have to find the derivative of e^{cos}Â ^{x}Â with the first principle method,

So, let f (x) = e^{cos}Â ^{x}

By using the first principle formula, we get,

^{}

**Solution:**

Exercise 11.2 Page No: 11.37

**Differentiate the following functions with respect to x:**

**1. Sin (3x + 5)**

**Solution:**

Given Sin (3x + 5)

**2. tan ^{2} x**

**Solution:**

Given tan^{2} x

**3. tan (x ^{o} + 45^{o})**

**Solution:**

Let y =Â tan (xÂ° + 45Â°)

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

**4. Sin (log x) **

**Solution:**

Given sin (log x)

**Solution:**

**6. e ^{tan x}**

**Solution:**

**7. Sin ^{2} (2x + 1)**

**Solution:**

Let y =Â sin^{2 }(2x + 1)

On differentiating y with respect to x, we get

**8. log _{7} (2x â€“ 3)**

**Solution:**

**9. tan 5x ^{o}**

**Solution:**

Let y =Â tan (5xÂ°)

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

**Solution:**

**Solution:**

**12. log _{x} 3**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**18. (log sin x) ^{2}**

**Solution:**

Let y =Â (log sin x)^{2}

**Solution:**

**Solution:**

**21. e ^{3x} cos 2x**

**Solution:**

**22. Sin (log sin x)**

**Solution:**

**23. e ^{tan 3x}**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**27. tan (e ^{sin x})**

**Solution:**

**Solution:**

**Solution:**

**30. log (cosec x â€“ cot x)**

**Solution:**

**Solution:**

**Solution:**

**33. tan ^{-1} (e^{x})**

**Solution:**

**Solution:**

**35. sin (2 sin ^{-1} x)**

**Solution:**

Let y =Â sin (2sin^{â€“1}x)

On differentiating y with respect to x, we get

**Solution:**

**Solution:**

Exercise 11.3 Page No: 11.62

**Differentiate the following functions with respect to x:**

**Solution:**

**Solution:**

**Solution:**

Let,

**Solution:**

Let,

**Solution:**

**Solution:**

**7. Sin ^{-1} (2x^{2} â€“ 1), 0 < x < 1**

**Solution:**

**8. Sin ^{-1} (1 â€“ 2x^{2}), 0 < x < 1**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

Solution:

**Solution:**

**Solution:**

Let,

**Solution: **

**Solution:**

**Solution:**

**Solution:**

Exercise 11.4 Page No: 11.74

**Find dy/dx in each of the following:**

**1. xy = c ^{2}**

**Solution:**

**2. y ^{3} â€“ 3xy^{2} = x^{3} + 3x^{2}y**

**Solution:**

Given y^{3}Â â€“ 3xy^{2}Â = x^{3}Â + 3x^{2}y,

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

**3. x ^{2/3} + y^{2/3} = a^{2/3}**

**Solution:**

Given x^{2/3} + y^{2/3} = a^{2/3},

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

**4. 4x + 3y = log (4x â€“ 3y)**

**Solution:**

Given 4x + 3y = log (4x â€“ 3y),

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

**Solution:**

**6. x ^{5} + y^{5} = 5xy**

**Solution:**

Given x^{5} + y^{5} = 5xy

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

**7. (x + y) ^{2} = 2axy**

**Solution:**

Given (x + y)^{2} = 2axy

**8. (x ^{2} + y^{2})^{2} = xy **

**Solution:**

Given (x + y)^{2} = 2axy

**9. Tan ^{-1} (x^{2} + y^{2})**

**Solution:**

Given tanÂ ^{â€“ 1}(x^{2}Â + y^{2}) = a,

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

**Solution:**

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

**Solution:**

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

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

**Solution:**

**Solution:**

**Solution:**

**Solution:**

Exercise 11.5 Page No: 11.88

**Differentiate the following functions with respect to x:**

**1. x ^{1/x}**

**Solution:**

**2. x ^{sin x}**

**Solution:**

**3. (1 + cos x) ^{x}**

**Solution:**

**Solution:**

**5. (log x) ^{x}**

**Solution:**

**6. (log x) ^{cos x}**

**Solution:**

Let y =Â (log x)^{cos x}

Taking log both the sides, we get

**7. (Sin x) ^{cos x}**

**Solution:**

**8. e ^{x log x}**

**Solution:**

**9. (Sin x) ^{log x}**

**Solution:**

**10. 10 ^{log sin x}**

**Solution:**

**11. (log x) ^{log x}**

**Solution:**

**Solution:**

**13. Sin (x ^{x})**

**Solution:**

**14. (Sin ^{-1} x)^{x}**

**Solution:**

^{}

**Solution:**

**16. (tan x) ^{1/x}**

**Solution:**

**Solution:**

**18. (i) (x ^{x}) âˆšx**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**18. (vi) e ^{sin x} + (tan x)^{x}**

**Solution:**

**18. (vii) (cos x) ^{x} + (sin x)^{1/x}**

**Solution:**

**Solution:**

**19. y = e ^{x} + 10^{x} + x^{x}**

**Solution:**

**20. y = x ^{n} + n^{x} + x^{x} + n^{n}**

**Solution:**

Exercise 11.6 Page No: 11.98

**Solution:**

**Solution:**

**Solution:**

**Solution:**

Exercise 11.7 Page No: 11.103

**Find dy/dx, when**

**1. x = at ^{2} and y = 2 at**

**Solution:**

**2. x = a (Î¸ + sin Î¸) and y = a (1 â€“ cos Î¸)**

**Solution:**

**3. x = a cos Î¸ and y = b sin Î¸**

**Solution:**

Given x = a cos Î¸ and y = b sin Î¸

**4. x = a e ^{Î¸} (sin Î¸ â€“ cos Î¸), y = a e^{Î¸} (sin Î¸ + cos Î¸)**

**Solution:**

**5. x = b sin ^{2} Î¸ and y = a cos^{2} Î¸**

**Solution:**

**6. x = a (1 â€“ cos Î¸) and y = a (Î¸ + sin Î¸) at Î¸ = Ï€/2**

**Solution:**

**Solution:**

**Solution:**

**9. x = a (cos Î¸ + Î¸ sin Î¸) and y = a (sin Î¸ â€“ Î¸ cos Î¸)**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

**Solution:**

Solution:

Exercise 11.8 Page No: 11.112

**1. Differentiate x ^{2} with respect to x^{3}.**

**Solution:**

**2. Differentiate log (1 +x ^{2}) with respect to tan^{-1} x.**

**Solution:**

**3. Differentiate (log x) ^{x} with respect to log x.**

**Solution:**

**4. Differentiate sin ^{-1} âˆš (1-x^{2}) with respect to cos^{-1}x, if**

**(i) x âˆˆ (0, 1)**

**(ii) x âˆˆ (-1, 0)**

**Solution:**

(i) Given sin^{-1} âˆš (1-x^{2})

(ii) Given sin^{-1} âˆš (1-x^{2})

**Solution:**

(i) Let

(ii) Let

(iii) Let

**Solution:**

**(i) x âˆˆ (0, 1/ âˆš2)**

**(ii) x âˆˆ (1/âˆš2, 1)**

**Solution:**

(i) Let

(ii) Let

**8. Differentiate (cos x) ^{sin x} with respect to (sin x)^{cos x}.**

**Solution:**

**Solution:**

**Solution:**

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