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 :