## anonymous one year ago 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)

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

8. anonymous

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

9. anonymous

Thank you!!!