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About Scotto
Expertise
Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.

Experience
Experience in the area: I have tutored students in all areas of mathematics for over 20 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

You are here: Experts > Teens > Homework/Study Tips > Calculus > composite functions

Topic: Calculus

Expert: Scotto
Date: 7/8/2008
Subject: composite functions

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.

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