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Thread: Derivative Chart and Composite Function

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    MHF Contributor Jason76's Avatar
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    Derivative Chart and Composite Function

    Derivative Chart and Composite Function-composite-function-chart.jpg

    I understand that $\displaystyle f(g(x))$ means $\displaystyle g(x)$ plugged into the function $\displaystyle f$ (at it's $\displaystyle x$ value). However we don't have the function, only a chart. How to get around this?
    Last edited by Jason76; Aug 26th 2013 at 05:38 PM.
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    Re: Derivative Chart and Composite Function

    Hey Jason76.

    Hint: Use the chain rule where h'(x) = g'(x)f'(g(x)) (What x corresponds to the one in line with h'(30))?
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    Re: Derivative Chart and Composite Function

    Quote Originally Posted by chiro View Post
    Hey Jason76.

    Hint: Use the chain rule where h'(x) = g'(x)f'(g(x)) (What x corresponds to the one in line with h'(30))?
    The answer is $\displaystyle 50$, but the chart seems to be saying $\displaystyle 30$ If you look at the line for $\displaystyle g(x)$ at $\displaystyle 30$, then you get $\displaystyle 20$
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    Re: Derivative Chart and Composite Function

    g(30) = 20, f(20) = 8 with derivatives:
    g'(30) = 10, f'(20) = 5 so this means

    h'(30) = g'(30)*f'(20) = 10*5 = 50.
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  5. #5
    MHF Contributor Jason76's Avatar
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    Re: Derivative Chart and Composite Function

    Quote Originally Posted by chiro View Post
    g(30) = 20, f(20) = 8 with derivatives:
    g'(30) = 10, f'(20) = 5 so this means

    h'(30) = g'(30)*f'(20) = 10*5 = 50.
    ok thanks. Makes sense.
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