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:

$\dfrac{d}{dx}sinh(x)=cosh(x)$

$\dfrac{d}{dx}x^n=nx^{n-1}$

$\dfrac{d}{dx}C=0$

Chain rule:

$\dfrac{d}{dx}[f(g(x))]=f'(g(x))g'(x)$

Where C is an arbitrary constant.

We have,

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

Differentiate with respect to x.

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

$f'(x)=\dfrac{2x}{cosh(f(x))}$

Therefore, the required values is $f'(x)=\dfrac{2x}{cosh(f(x))}$.