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.
(a)
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.
(a)    
g'(π/3)

anonymous · Answer

and h'(pi/3)
I found g' but im having a difficult time with h'

anonymous · Answer

Well, we would just need to do a quotient rule and find the derivative of h(x). Did you try doing that?

anonymous · Answer

yeah but i got it wrong, im not sure what i did

anonymous · Answer

Well, derivative of cos(x) is -sin(x) and derivative of f(x) is f'(x). So following quotient rule we have
$$h'(x) = \frac{ -\sin(x)f(x)-\cos(x)f'(x) }{ [f(x)]^{2} }$$ Now we justplug in pi/3

anonymous · Answer

Im confused, i would plug in pi/3 for the x, or the values that i was given?

anonymous · Answer

Plug in pi/3 into every x in h'(x)

anonymous · Answer

would my answer be (5/18)-3root3/18?

anonymous · Answer

Yes. And of course the 3root3/18 goes root3/6

anonymous · Answer

Thank you!!!