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Calculus/composite functions

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Expert: Scotto - 7/8/2008


Question
Hi....I am working on a composite function question and i am sort of lost.  The question is:
Let K(x) be a composite function defined as K(x)=F(G(x)). Find K'(3) if:
Then they give a table of values

X    F(x)     F'(x)     G(x)      G'(x)
1      2        .5       -3        5
2      3        1         0        4
3      4        2         2        3
4      6        4         3        .5

I am confused as to how to start.  Should I be able to figure out what the function is?  Any help is greatly appreciated.  Thank you. Steph

Answer
This looks like one of those problems where they supply so much information so that people get confused.  You really don't need it all.

If K(x) = F(G(x)), then by the chain rule, K'(x)=F'(G(x))G'(x).  

Find G(3) and G'(3), and then find y=G(3), then find F'(y).
Now that you have F' and G' when x=3, multiply for the answer.

Thanks for the wonderful question.

Calculus

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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