Question

Find f' in terms of g' of f(x)=g(x)(x-a)

Answer 1

Solution:

Given, $f(x)=g(x)(x-a)$

On differentiating both sides w.r.t $x$ ,

$f'(x)=[g(x)]'(x-a)+g(x)(x-a)'$ [Using product rule]

$\Rightarrow f'(x)=g'(x)(x-a)+g(x)(1-0)$

$\Rightarrow f'(x)=g'(x)(x-a)+g(x)$