Suppose and are functions having second derivatives and everywhere

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

Problem

Suppose

f

and

g

are functions having second derivatives

f''

and

g''

everywhere. If

f(x)g(x)=1

for all

x

and

f'

and

g'

are never zero, then

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

equals. (a)

-\frac{2f'(x)}{f(x)}

(b)

-\frac{2g'(x)}{g(x)}

(c)

-\frac{f'(x)}{f(x)}

(d)

\frac{2f'(x)}{f(x)}