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

1. ## 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.

2. 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!

3. Originally Posted by Scott H
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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# if h(x) = f(g(x)), find h'(3).

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