AP Calculus AB and BC glossary

Composite function

Also called: Function composition

A composite function is one function evaluated inside another, so the output of the inner function becomes the input of the outer one. Spotting a composition is what tells you to use the chain rule.

(f \circ g)(x) = f(g(x))

The practical test is to ask what you would compute last if you evaluated the expression by hand. In $\sin(x^2)$ you would square first and take the sine last, so the outer function is sine and the inner function is $x^2$ .

The mistake

Reading a product as a composition. In $x^2 \sin x$ nothing is fed into anything, so that is the product rule, not the chain rule.

Appears in: Unit 3: Chain Rule, Implicit, and Inverses