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

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

**Solution:**

We have,

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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.