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

Chapter 11 of RD Sharma's Class 12 Mathematics textbook covers Differentiation, a fundamental concept in calculus. Exercise 11.2 Set 2 typically focuses on more advanced differentiation techniques, including the differentiation of composite functions, implicit differentiation, and applications of various differentiation rules.

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

Summary

Exercise 11.2 Set 2 in Chapter 11 of RD Sharma's Class 12 Mathematics provides a more challenging set of problems on differentiation. These questions typically involve composite functions, trigonometric functions, exponential and logarithmic functions, and combinations thereof. This set helps students apply multiple differentiation rules simultaneously and prepares them for more complex mathematical analysis.