# Class 11 RD Sharma Solutions – Chapter 30 Derivatives – Exercise 30.4 | Set 1

• Last Updated : 16 May, 2021

### Question 1. Differentiate x3 sin x with respect to x.

Solution:

We have,

=> y = x3 sin x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

= sinx (3x2) + x3 (cosx)

= 3x2 sinx + x3 cosx

= x2 (3 sinx + x cos x)

### Question 2. Differentiate x3 ex with respect to x.

Solution:

We have,

=> y = x3 ex

On differentiating both sides with respect to x, we get,

On using product rule, we get,

= ex (3x2) + x3 (ex)

= 3x2 ex + x3 ex

= x2 ex (3 + x)

### Question 3. Differentiate x2 ex log x with respect to x.

Solution:

We have,

=> y = x2 ex log x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

On using product rule again in the second part of the expression, we get,

### Question 4. Differentiate xn tan x with respect to x.

Solution:

We have,

=> y = xn tan x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

### Question 5. Differentiate xn loga x with respect to x.

Solution:

We have,

=> y = xn loga x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

### Question 6. Differentiate (x3+x2+1)sinx with respect to x.

Solution:

We have,

=> y =

On differentiating both sides with respect to x, we get,

On using product rule, we get,

### Question 7. Differentiate sin x cos x with respect to x.

Solution:

We have,

=> y = sin x cos x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

= cos x (cos x) − sin x (−sin x)

= cos2 x − sin2 x

= cos2 x − (1 − cos2 x)

= cos2 x − 1 + cos2 x

= 2 cos2 x − 1

= cos 2x

### Question 8. Differentiate  with respect to x.

Solution:

We have,

=> y =

=> y =

On differentiating both sides with respect to x, we get,

On using product rule, we get,

On using product rule again in the second part of the expression, we get,

### Question 9. Differentiate x2 sin x log x with respect to x.

Solution:

We have,

=> y = x2 sin x log x

On differentiating both sides with respect to x, we get,

On using product rule, we get,

On using product rule again in the second part of the expression, we get,

### Question 10. Differentiate x5 ex + x6 log x with respect to x.

Solution:

We have,

=> y = x5 ex + x6 log x

On differentiating both sides with respect to x, we get,

On using chain rule, we get,

On using product rule, we get,

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