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.

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- Oct 17th 2009, 10:24 AMyoman360Find 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 AMScott 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 AMyoman360