RD Sharma Solutions for Class 11 Chapter 30 - Derivatives Exercise 30.3

Exercise 30.3 mainly deals with fundamental rules for differentiation which includes theorems with examples. The theorems are explained in a clear manner to help students to understand the concepts well. Students can solve the exercise-wise problems by referring to the solutions to gain a better hold on these concepts. RD Sharma Class 11 Maths Solutions provided here are formulated by subject experts to help students gain that extra edge of knowledge. The RD Sharma Solutions are made readily available in PDF format which can be downloaded easily from the links given below.

RD Sharma Solutions for Class 11 Maths Exercise 30.3 Chapter 30 – Derivatives

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Exercise 30.1 Solutions

Exercise 30.2 Solutions

Exercise 30.4 Solutions

Exercise 30.5 Solutions

Access answers to RD Sharma Solutions for Class 11 Maths Exercise 30.3 Chapter 30 – Derivatives

EXERCISE 30.3 PAGE NO: 30.33

Differentiate the following with respect to x:

1. x⁴ – 2sin x + 3 cos x

Solution:

Given:

f (x) = x⁴ – 2sin x + 3 cos x

Differentiate on both sides with respect to x, and we get

2. 3^x + x³ + 3³

Solution:

Given:

f (x) = 3^x + x³ + 3³

Differentiate on both sides with respect to x, and we get

Solution:

Given:

Differentiate on both sides with respect to x, and we get

4. e^{x log a} + e^{a log x} + e^{a log a}

Solution:

Given:

f (x) = e^{x log a} + e^{a log x} + e^{a log a}

We know that,

e^{log f(x)} = f(x)

So,

f(x) = a^x + x^a + a^a

Differentiate on both sides with respect to x,  and we get

5. (2x² + 1) (3x + 2)

Solution:

Given:

f (x) = (2x² + 1) (3x + 2)

= 6x³ + 4x² + 3x + 2

Differentiate on both sides with respect to x, and we get