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

• Oct 17th 2009, 10:24 AM
yoman360
Find h'(3) if h(x)=g(f(x))
Using the table of values Find h'(3) if h(x)=g(f(x))
http://i595.photobucket.com/albums/t...leofvalues.jpg

I feel so dumb right now because this problem looks super easy but I can't get the correct answer.
• Oct 17th 2009, 10:35 AM
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! :)
• Oct 17th 2009, 10:47 AM
yoman360
Quote:

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(Rofl)