Practice Chain Rule in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The derivative of a composite function f(g(x)) equals f'(g(x)) \cdot g'(x): the derivative of the outer function evaluated at the inner, times the derivative of the inner.

Derivative of outside times derivative of inside. Unpack layers.

Example 1

easy
Find the derivative of f(x) = (3x + 1)^4.

Example 2

medium
Find the derivative of f(x) = (x^2 + 1)^5.

Example 3

hard
Find the derivative of f(x) = \sin(x^3).

Example 4

easy
Find the derivative of f(x) = (5x - 2)^3.

Example 5

medium
Find the derivative of f(x) = \sqrt{4x + 3}.