Practice Differentiation Rules in Math

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

Quick Recap

A set of standard formulas for finding derivatives of common function types without using the limit definition each time.

Shortcuts so you don't have to use the limit definition every time.

Example 1

easy
Use the product rule to differentiate f(x) = x^3 \cdot \sin x.

Example 2

medium
Use the quotient rule to differentiate f(x) = \dfrac{x^2 + 1}{x - 3}.

Example 3

easy
Differentiate f(x) = x^2 \cos x using the product rule.

Example 4

hard
Differentiate f(x) = \dfrac{e^x}{x^2 + 1} using the quotient rule.