# RD Sharma Class 12 Ex 11.2 Solutions Chapter 11 Differentiation

Here we provide RD Sharma Class 12 Ex 11.2 Solutions Chapter 11 Differentiation for English medium students, Which will very helpful for every student in their exams. Students can download the RD Sharma Class 12 Ex 11.2 Solutions Chapter 11 Differentiation book pdf download. Now you will get step-by-step solutions to each question.

## RD Sharma Class 12 Ex 11.2 Solutions Chapter 11 Differentiation

### 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 = esin √xwith respect to x.

Solution:

We have,

y = esin √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 = etan x with respect to x.

Solution:

We have,

y = etan 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 = logx 3 with respect to x.

Solution:

We have,

y = logx 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 = etan 3x with respect to x.

Solution:

We have,

y = etan 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

### Question 25. 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 26. Differentiate y =  with respect to x.

Solution:

We have,

y =

y =

As , we get

y =

On differentiating y with respect to x we get,

On using chain rule, we have

On using quotient rule, we have

### Question 27. 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 28. Differentiate y =  with respect to x.

Solution:

We have,

I =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 29. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule, we have

On using product rule, we have

### Question 30. 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 31. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule and chain rule, we get

### Question 32. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule and chain rule, we get

### Question 33. 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 34. 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 35. 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 36. 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 37. Differentiate y =  with respect to x.

Solution:

We have,

y =

y =

On differentiating y with respect to x we get,

On using chain rule, we have

### Question 38. 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 39. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule, we have

On using product rule and chain rule, we have

### Question 40. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using product rule and chain rule, we have

### Question 41. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using product rule and chain rule, we have

### Question 42. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule, chain rule and product rule we get,

### Question 43. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule, we get

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

### Question 44. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using product rule and chain rule, we have

### Question 45. Differentiate y =  with respect to x.

Solution:

We have,

y =

On rationalizing we get,

y =

y =

y =

y =

y =

y =

On differentiating y with respect to x we get,

### Question 46. 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 47. 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 chain rule again, we have

### Question 48. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using chain rule and quotient rule, we get

### Question 49. Differentiate y =  with respect to x.

Solution:

We have,

y =

On differentiating y with respect to x we get,

On using quotient rule, we get

On using product rule, we get

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