Question

If y=log(x^2-a^2) then prove that y"' = 2[1/(x+a)^3 + 1/(x-a)^3]​

Answer 1

ANSWER

Given, x=sin

−1

t or sinx=t

and y=log(1−t

2

)

=log(1−sin

2

x)

=log(cos

2

x)

Hence, y=2log( cosx)

Therefore,

dx

dy

=

cosx

−2sinx

=−2tanx

dx

2

d

2

y

=−2sec

2

x=

cos

2

x

−2

=

1−sin

2

x

−2

=

1−t

2

−2

Hence,

dx

2

d

2

y

∣

t=

2

1

=

1−(

2

1

)

2

−2

=

1−

4

1

−2

=

4−1

−8

=

3

−8

.

see the image if u can't understand..... helpful for you