Class 12 RD Sharma Solutions - Chapter 11 Differentiation - Exercise 11.2 | Set 3

Question 50. 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 get

Question 51. 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 52. 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 53. 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

Question 54. 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

Question 55. 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

Question 56. 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

Question 57. Differentiate y =  with respect to x.

Solution:

We have,

y = 

y = 

y = 

y = 

On differentiating y with respect to x we get,

Question 58. If , show that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

On using chain rule, we get

Hence, proved.

Question 59. If y =  , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 60. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

As , we have

Hence proved.

Question 61. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 62. If y = , prove that .

Solution:

We have,

y = 

y = 

y = 

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 63. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 64. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

As we have , we get

Hence proved.

Question 65. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

As y = , we have

Hence proved.

Question 66. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 67. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 68. If y = , prove that .

Solution:

We have,

y = 

y = 

y = 

y = 

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 69. If y = , prove that .

Solution:

We have,

y = 

On differentiating y with respect to x we get,

Hence proved.

Question 70. If y = , prove that .

Solution:

We have,

y = 

On squaring both sides we get,

On differentiating both sides with respect to x we get,

Hence proved.

Question 71. If y = , prove that .

Solution:

We have,

y = 

On differentiating both sides with respect to x we get,

On using chain rule, we get 

As , we get

Hence proved.

Question 72. If y = , prove that .

Solution:

We have,

y = 

On squaring both sides we get,

On differentiating both sides with respect to x we get,

Hence proved.

Question 73. If xy = 4, prove that .

Solution:

We have,

xy = 4

y = 

On differentiating both sides with respect to x we get,

As x = , we get

On dividing both sides by x, we get

Hence proved.

Question 74. Prove that .

Solution:

We have,

L.H.S. = 

= 

= 

= 

= 

= 

= 

= 

= 

= 

= 

= 

= 

= R.H.S.

Hence proved.