RD Sharma Solutions for Class 11 Chapter 30 - Derivatives Exercise 30.1

Here, in this exercise, we shall discuss concepts related to derivative at a point where the answers are explained with suitable examples for students to understand clearly. Students can make use of RD Sharma Class 11 Maths Solutions to obtain good marks in the board examination. Subject experts have designed the solutions in a step by step manner to help students understand the concepts and score well in the exams. The pdf of RD Sharma Solutions are provided in the links given below, which can be downloaded easily and can be used for future reference as well.

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Also, access other exercises of RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives

Exercise 30.2 Solutions

Exercise 30.3 Solutions

Exercise 30.4 Solutions

Exercise 30.5 Solutions

Access answers to RD Sharma Solutions for Class 11 Maths Exercise 30.1 Chapter 30 – Derivatives

EXERCISE 30.1 PAGE NO: 30.3

1. Find the derivative of f(x) = 3x at x = 2

Solution:

Given:

f(x) = 3x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 1

2. Find the derivative of f(x) = x2 – 2 at x = 10

Solution:

Given:

f(x) = x2 – 2

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 2

= 0 + 20 = 20

Hence,

Derivative of f(x) = x2 – 2 at x = 10 is 20

3. Find the derivative of f(x) = 99x at x = 100.

Solution:

Given:

f(x) = 99x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 3

4. Find the derivative of f(x) = x at x = 1

Solution:

Given:

f(x) = x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 4

5. Find the derivative of f(x) = cos x at x = 0

Solution:

Given:

f(x) = cos x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 5

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 6

6. Find the derivative of f(x) = tan x at x = 0

Solution:

Given:

f(x) = tan x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 7

7. Find the derivatives of the following functions at the indicated points:
(i) sin x at x = π/2
(ii) x at x = 1

(iii) 2 cos x at x = π/2

(iv) sin 2xat x = π/2

Solution:

(i) sin x at x = π/2

Given:

f (x) = sin x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 8

[Since it is of indeterminate form. Let us try to evaluate the limit.]

We know that 1 – cos x = 2 sin2(x/2)

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 9

(ii) x at x = 1

Given:

f (x) = x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 10

(iii) 2 cos x at x = π/2

Given:

f (x) = 2 cos x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 11

(iv) sin 2xat x = π/2

Solution:

Given:

f (x) = sin 2x

By using the derivative formula,

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 12

[Since it is of indeterminate form. We shall apply sandwich theorem to evaluate the limit.]

Now, multiply numerator and denominator by 2, we get

RD Sharma Solutions for Class 11 Maths Chapter 30 – Derivatives - image 13

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