If g(x) is the inverse function f(x) and f'(x)={1}{1+x^{4}} then g'(x) is

Correct Answer is : 1+[g(x)]41+[g(x)]^{4}1+[g(x)]4

Correct Answer is : 1+[g(x)]41+[g(x)]^{4}1+[g(x)]4

Test Index

UPSC NDA Math Model Paper 8

Question : 111 of 120

Marks: +1, -0

g(x)

f(x)

f'(x)=\frac{1}{1+x^{4}}

g'(x)

Solution:

Given:

g(x)

is the inverse function

f(x)

Therefore,

g(x)=f^{-1}(x)

\Rightarrow f[g(x)]=x

Differenating with respect to

x

, we get

\Rightarrow f'[g(x)] \times g'(x)=1

\therefore g'(x)=\frac{1}{f'[g(x)]}

Given:

f'(x)=\frac{1}{1+x^{4}}

Replace

x

g(x)

f'[g(x)]=\frac{1}{1+[g(x)]^{4}}

Put in the value of

f'[g(x)]

in equation (1), we get

Hence,

g'(x)=1+[g(x)]^{4}

Go to Question:

Prev Question

Next Question