RD Sharma Solutions for Class 11 Chapter 30 - Derivatives Exercise 30.4

This exercise deals with fundamental rules for differentiation which are based on the product rule for differentiation. The solutions here are created by the team of expert faculty at BYJU’S. Students can practice these problems in the most efficient ways and can also focus on cracking the solutions of Maths in such a way that it is easy for them to understand. RD Sharma Class 11 Maths Solutions mainly aims at equipping the students with detailed and step-wise explanations for all the answers to the questions given in the exercises of this Chapter. The PDF of RD Sharma Solutions can be downloaded from the links given below.

RD Sharma Solutions for Class 11 Maths Exercise 30.4 Chapter 30 – Derivatives

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Access answers to RD Sharma Solutions for Class 11 Maths Exercise 30.4 Chapter 30 – Derivatives

EXERCISE 30.4 PAGE NO: 30.39

Differentiate the following functions with respect to x:

1. x³ sin x

Solution:

Let us consider y = x³ sin x

We need to find dy/dx

We know that y is a product of two functions, say u and v, where,

u = x³ and v = sin x

∴ y = uv

Now let us apply the product rule of differentiation.

By using the product rule, we get

2. x³ e^x

Solution:

Let us consider y = x³ e^x

We need to find dy/dx

We know that y is a product of two functions, say u and v, where,

u = x³ and v = e^x

∴ y = uv

Now let us apply the product rule of differentiation.

By using the product rule, we get

3. x² e^x log x

Solution:

Let us consider y = x² e^x log x

We need to find dy/dx

We know that y is a product of two functions, say u and v, where,

u = x² and v = e^x

∴ y = uv

Now let us apply the product rule of differentiation.

By using the product rule, we get

4. xⁿ tan x

Solution:

Let us consider y = xⁿ tan x

We need to find dy/dx

We know that y is a product of two functions, say u and v, where,

u = xⁿ and v = tan x

∴ y = uv

Now let us apply the product rule of differentiation.

By using the product rule, we get

5. xⁿ log_a x

Solution:

Let us consider y = xⁿ log_a x

We need to find dy/dx

We know that y is a product of two functions, say u and v, where,

u = xⁿ and v = log_a x

∴ y = uv

Now let us apply the product rule of differentiation.

By using the product rule, we get