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