Question

Suppose
f(π/3) = 5 and f '(π/3) = −7,
and let
g(x) = f(x) sin x
and
h(x) = (cos x)/f(x).
FIND: g'(pi/3) AND h'(pi/3)

Answer 1

\[g(x)=f(x)\sin(x)\]
\[g'(x)=f'(x)\sin(x)+f(x)\cos(x)\] by the product rule,
replace
\[x=\frac{\pi}{3}\] and see what number you get

Answer 2

\[g'(\frac{\pi}{3})=f'(\frac{\pi}{3})\sin(\frac{\pi}{3})+f(\frac{\pi}{3})\cos(\frac{\pi}{3})\]etc