Which of the following gives the derivative of where and are differentiable and ?

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Which of the following gives the derivative of

\dfrac{f(x)}{g(x)}

where

f

and

g

are differentiable and

g(x)\neq 0

? (a)

\dfrac{f'(x)g(x)+f(x)g'(x)}{[g(x)]^{2}}

(b)

\dfrac{f'(x)}{g'(x)}

(c)

\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}}

(d)

\dfrac{f'(x)g(x)-f(x)g'(x)}{g(x)}