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

• Last Updated : 14 Jul, 2021

### Question 50. Differentiate y =  with respect to x.

Solution:

We have,

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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.

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