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let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=...

let `f(x)=e^x ,g(x)=sin^(- 1) x `and `h(x)=f(g(x))` then find `(h^(prime)(x))/(h(x))`

A

`e^(sin^(-1)x)`

B

`(1)/(sqrt(1 - x^(2)))`

C

`(1)/(sqrt(1 - x^(2)))`

D

`(1)/(1 - x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Given ` y = log ((1 - x^(2))/(1 + x^(2)))`
and ` h(x) = f[ g(x) ] rArr `
` h(x) = f(sin^(-1) x) = e^(sin^(-1)x)`
` therefore h(x) = e^(sin^(-1)x)`
` rArr h'(x) = e^(sin^(-1)x) (1)/(sqrt(1 - x^(2)))`
` rArr (h'(x))/(h(x))= (1)/(sqrt(1 - x^(2)))`
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