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
easyFind the derivative of f(x) = (3x + 1)^4.
Example 2
mediumFind the derivative of f(x) = (x^2 + 1)^5.
Example 3
hardFind the derivative of f(x) = \sin(x^3).
Example 4
easyFind the derivative of f(x) = (5x - 2)^3.
Example 5
mediumFind the derivative of f(x) = \sqrt{4x + 3}.