# Exercise 11.2

Question 1

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 2

Differentiate

Sol :

Let

which can be written as

Differentiating y with respect to x we get,

So,

Question 3

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 4

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 5

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 6

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 7

Differentiate

Sol :

Let

which can be written as

Differentiating y with respect to x we get,

So,

Question 8

Differentiate

Sol :

Let

Let

Differentiating y with respect to x we get,

So,

Question 9

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 10

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 11

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 12

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 13

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 14

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 15

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 16

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

on rationalising

So,

Question 17

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 18

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 19

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 20

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 21

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 22

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 23

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 24

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 25

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 26

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 27

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 28

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 29

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 30

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

taking cosec x common

= cosec x

So,

Question 31

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 32

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 33

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 34

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 35

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 36

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 37

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 38

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 39

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

taking common and

So,

Question 40

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 41

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 42

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 43

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 44

Differentiate

Sol :

Let

Differentiating y with respect to x we get,

So,

Question 45

Differentiate

Sol :

on rationalising , we get

=\dfrac{\sqrt{x^2+1}+\sqrt{x^2-1}}{\sqrt{x^2+1}-\sqrt{x^2-1}}\times \dfrac{\sqrt{x^2+1}+\sqrt{x^2-1}}{\sqrt{x^2+1}+\sqrt{x^2-1}}

=\dfrac{\left(\sqrt{x^2+1}+\sqrt{x^2-1}\right)^2}{\left(\sqrt{x^2+1}\right)^2-\left(\sqrt{x^2-1}\right)^2}

Let

Differentiating y with respect to x we get,

So,

Question 46

Differentiate

Sol :

Question 47

Differentiate

Sol :

Question 48

Differentiate

Sol :

Question 49

Differentiate

Sol :

Question 50

Differentiate

Sol :

Question 51

Differentiate

Sol :

Question 52

Differentiate

Sol :

Question 53

Differentiate

Sol :

Question 54

Differentiate

Sol :

Question 55

Differentiate

Sol :

Question 56

Differentiate

Sol :

Question 57

Differentiate

Sol :

Question 58

Differentiate

Sol :