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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)

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  1. anonymous
    • one year ago
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    and h'(pi/3) I found g' but im having a difficult time with h'

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

  3. anonymous
    • one year ago
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    yeah but i got it wrong, im not sure what i did

  4. anonymous
    • one year ago
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    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
    • one year ago
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    Im confused, i would plug in pi/3 for the x, or the values that i was given?

  6. anonymous
    • one year ago
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    Plug in pi/3 into every x in h'(x)

  7. anonymous
    • one year ago
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    would my answer be (5/18)-3root3/18?

  8. anonymous
    • one year ago
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    Yes. And of course the 3root3/18 goes root3/6

  9. anonymous
    • one year ago
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    Thank you!!!

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