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Thread: Find h'(3) if h(x)=g(f(x))

  1. #1
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    Find h'(3) if h(x)=g(f(x))

    Using the table of values Find h'(3) if h(x)=g(f(x))


    I feel so dumb right now because this problem looks super easy but I can't get the correct answer.
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  2. #2
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    To find the answer, we use the Chain Rule. This states that if

    $\displaystyle h(x)=g(f(x)),$

    then

    $\displaystyle h'(x)=g'(f(x))f'(x).$

    A way of looking at this rule is to note that $\displaystyle f$ influences how fast $\displaystyle f(x)$ changes with $\displaystyle x$, which in turn affects the rate of change of $\displaystyle g(f(x))$ by a factor of $\displaystyle f'(x)$.

    If $\displaystyle f(x)=2x$, for example, then $\displaystyle f(x)$ will change twice as fast as $\displaystyle x$, and the rate of change of $\displaystyle g(f(x))$ will be multiplied by a factor of $\displaystyle 2$.

    Hope this helps!
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  3. #3
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    Quote Originally Posted by Scott H View Post
    To find the answer, we use the Chain Rule. This states that if

    $\displaystyle h(x)=g(f(x)),$

    then

    $\displaystyle h'(x)=g'(f(x))f'(x).$

    A way of looking at this rule is to note that $\displaystyle f$ influences how fast $\displaystyle f(x)$ changes with $\displaystyle x$, which in turn affects the rate of change of $\displaystyle g(f(x))$ by a factor of $\displaystyle f'(x)$.

    If $\displaystyle f(x)=2x$, for example, then $\displaystyle f(x)$ will change twice as fast as $\displaystyle x$, and the rate of change of $\displaystyle g(f(x))$ will be multiplied by a factor of $\displaystyle 2$.

    Hope this helps!
    Thanks that helped. I feel dumb b/c that was super easy and did not know how to do it. But now I do. Thanks
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