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Math Help - Composite Derivative

  1. #1
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    Composite Derivative

    let f and g be differentiable functions such that

    f(1)=4, g(1)=3, f '(3)=-5, f '(1)=-4, g '(1)=-3, g '(3)=2

    if h(x)=f(g(x)), then h '(1)= ?

    please help
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  2. #2
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    Quote Originally Posted by rawkstar View Post
    let f and g be differentiable functions such that

    f(1)=4, g(1)=3, f '(3)=-5, f '(1)=-4, g '(1)=-3, g '(3)=2

    if h(x)=f(g(x)), then h '(1)= ?

    please help
    h(x) = f[g(x)]

    h'(x) = f'[g(x)] \cdot g'(x)

    h'(1) = f'[g(1)] \cdot g'(1)

    h'(1) = f'(3) \cdot g'(1) = (-5) \cdot (-3) = 15
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    Great! Thank you!
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