# 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

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

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!

3. Originally Posted by Scott H
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