Barrons AP Calculus - David Bock

C. THE CHAIN RULE; THE DERIVATIVE OF A COMPOSITE

FUNCTION

Formula (3) says that

This formula is an application of the Chain Rule. For example, if we use formula (3) to find the
derivative of (x^2 − x + 2)^4 , we get

In this last equation, if we let y = (x^2 − x + 2)^4 and let u = x^2 − x + 2, then y = u^4. The preceding
derivative now suggests one form of the Chain Rule: