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Math Help - 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

    h(x)=g(f(x)),

    then

    h'(x)=g'(f(x))f'(x).

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

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

    h(x)=g(f(x)),

    then

    h'(x)=g'(f(x))f'(x).

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

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