Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.2 | Set 1

Question 1. Differentiate y = sin (3x + 5) with respect to x.

Solution:

We have,

y = sin (3x + 5)

On differentiating y with respect to x we get,

On using chain rule, we have

Question 2. Differentiate y = tan² x with respect to x.

Solution:

We have,

y = tan² x

On differentiating y with respect to x we get,

On using chain rule, we have

Question 3. Differentiate y = tan (x + 45°) with respect to x.

Solution:

We have,

y = tan (x + 45°)

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 4. Differentiate y = sin (log x) with respect to x.

Solution:

We have,

y = sin (log x)

On differentiating y with respect to x we get,

On using chain rule, we have

Question 5. Differentiate y = e^{sin √x} with respect to x.

Solution:

We have,

y = e^{sin √x}

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

Question 6. Differentiate y = e^{tan x} with respect to x.

Solution:

We have,

y = e^{tan x}

On differentiating y with respect to x we get,

On using chain rule, we have

Question 7. Differentiate y = sin² (2x + 1) with respect to x. 

Solution:

We have,

y = sin² (2x + 1)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

As sin 2A = 2 sin A cos A, we get

Question 8. Differentiate y = log₇ (2x − 3) with respect to x.

Solution:

We have,

y = log₇ (2x − 3)

As , we have

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 9. Differentiate y = tan 5x° with respect to x.

Solution:

We have,

y = tan 5x°

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 10. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 11. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 12. Differentiate y = log_x 3 with respect to x.

Solution:

We have,

y = log_x 3

As , we get

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

As , we get

Question 13. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 14. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 15. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 16. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 17. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

Question 18. Differentiate y = (log sin x)² with respect to x.

Solution:

We have,

y = (log sin x)²

On differentiating y with respect to x we get,

On using chain rule, we have

Question 19. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

Question 20. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

Question 21. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using product rule, we have

On using chain rule, we have

Question 22. Differentiate y = sin(log sin x) with respect to x.

Solution:

We have,

y = sin(log sin x)

On differentiating y with respect to x we get,

On using chain rule, we have

On using chain rule again, we have

Question 23. Differentiate y = e^{tan 3x} with respect to x.

Solution:

We have,

y = e^{tan 3x}

On differentiating y with respect to x we get,

On using chain rule, we have

Question 24. Differentiate y =  with respect to x.

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we have