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Math Help - Chain Rule

  1. #1
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    Chain Rule

    Let f(3) = 1, g(2) = 3, f'(3) = 4, g'(2) = 5. If h(x) = f(g(x)), find h'(2).


    My professor got 20 for this. Why would you ignore g(2)?

    Wouldn't it be 4*3 * 5?
    Because the chain rule is f'(g(x)) * g'(x)
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  2. #2
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    Re: Chain Rule

    Quote Originally Posted by habibixox View Post
    Let f(3) = 1, g(2) = 3, f'(3) = 4, g'(2) = 5. If h(x) = f(g(x)), find h'(2).


    My professor got 20 for this. Why would you ignore g(2)?

    Wouldn't it be 4*3 * 5?
    Because the chain rule is f'(g(x)) * g'(x)
    h(x) = f[g(x)]

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

    h'(2) = f'[g(2)] \cdot g'(2)

    note that g(2) = 3 is substituted into the f' term ...

    h'(2) = f'(3) \cdot g'(2)

    h'(2) = 4 \cdot 5 = 20
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