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.