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

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• 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

\$\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! :)
• 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

\$\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(Rofl)