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)

Answer 1

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

Answer 2

Then just plug in \(x=\pi/3\).

Answer 3

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

Answer 4

You mixed \(f'\) with \(f\)

Answer 5

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.

Answer 6

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

Answer 7

I'd try it.

Answer 8

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