Suppose f(π/3) = 3 and f '(π/3) = −5, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following: g'(π/3)

Question

Suppose f(π/3) = 3 and f '(π/3) = −5, and let g(x) = f(x) sin x and h(x) = (cos x)/f(x). Find the following:  g'(π/3)

anonymous · Answer

Use product rule: $$
g'(x) = f'(x)\sin(x)+f(x)\cos(x)
$$

anonymous · Answer

Then just plug in $x=\pi/3$.

anonymous · Answer

I get
7/2 - 5 sqrt (3/2) but this is given by the program as incorrect. Any further assistance?

anonymous · Answer

You mixed $f'$ with $f$

anonymous · Answer

ah. Would the answer then be 3/2 - (5 sqrt 3)/2  ?

Down to my last try so I'd rather not get it wrong. But you are right I confused the two f's before.

anonymous · Answer

$$
g'(x) = (-5)(\sqrt{3}/2)+(3)(1/2)=3/2-5\sqrt{3}/2
$$

anonymous · Answer

I'd try it.

anonymous · Answer

It was correct. Thank you very much good sir, I was stuck. I really need more sleep.
You can has medal