# Class 12 RD Sharma Solutions – Chapter 11 Differentiation – Exercise 11.2 | Set 2

**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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