Applying the Chain Rule

Calculus 1 · Axiom Academy

EXAMPLE Chain Rule Application Differentiating a composite function: peel off the outer function, then the inner. Find the derivative . This is a composite function — a sine wrapped around a cube — so the chain rule applies. Nicely done. You differentiated a composite function by working from the outside in. Spot the composition: is an outer function evaluated at an inner function u = x^ 3 . Chain rule: — the outer derivative (with the inner left inside) times the inner derivative. Every time a function is nested inside another, the chain rule lets you differentiate the layers one at a time and multiply the pieces together.

This is the written version of the interactive lesson above. See the full Calculus 1 course.