Mathematics

Problem

m(t)=\dfrac{g'(t)}{f'(t)}

for differentiable functions

f

and

g

with

f'(t)\neq0

, which of the following is the correct expression for

\dfrac{dm}{dt}

? a)

\displaystyle \frac{f'(t)g''(t)+g'(t)f''(t)}{[f'(t)]^{2}}

\displaystyle \frac{g'(t)f''(t)-f'(t)g''(t)}{[f'(t)]^{2}}

\displaystyle \frac{f'(t)g''(t)-g'(t)f''(t)}{[f'(t)]^{2}}

\displaystyle \frac{g''(t)}{f'(t)}