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# 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,    Attention reader! All those who say programming isn’t for kids, just haven’t met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

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