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

• Last Updated : 14 Jul, 2021

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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