Question

Suppose
f(π/3) = 4 and f '(π/3) = −7,
and let
g(x) = f(x) sin x
and
h(x) = (cos x)/f(x).
Find the following.
a. g'(π/3)
b. h'(π/3)

Answer 1

\[\Large\bf\sf h(x)\quad=\quad \frac{\cos x}{f(x)}\]
\[\Large\bf\sf h'(x)\quad=\quad \frac{\color{royalblue}{\left[\cos x\right]'}f(x)-\cos x\color{royalblue}{\left[f(x)\right]'}}{f(x)^2}\]We need to apply quotient rule for this problem.
Understand how I set that up?
We need to take the derivative of the blue parts.

Answer 2

Can you elaborate?