Question

What's the right answer?

Answer 1

Given:

`sinh(f(x))=1+x^2`

To find:

The value of f'(x).

Solution:

Formulae used:

`(d)/(dx)sinh(x)=cosh(x)`

`(d)/(dx)x^n=nx^(n-1)`

`(d)/(dx)C=0`

Chain rule:

`(d)/(dx)[f(g(x))]=f'(g(x))g'(x)`

Where C is an arbitrary constant.

We have,

`sinh(f(x))=1+x^2`

Differentiate with respect to x.

`cosh(f(x))f'(x)=0+2x`

`f'(x)=(2x)/(cosh(f(x)))`

Therefore, the required values is
`f'(x)=(2x)/(cosh(f(x)))`.