Practice Derivative in Math

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

Quick Recap

The instantaneous rate of change of a function at a single point, defined as the limit of the slope of secant lines.

How fast is the output changing right now? The slope of the curve at each point.

Example 1

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

Example 2

medium
Find the derivative of f(x) = x^3 - 4x^2 + 7x and evaluate f'(2).

Example 3

hard
Use the limit definition to find the derivative of f(x) = x^2.

Example 4

easy
Find the derivative of f(x) = 7x^4 - 2x + 9.

Example 5

hard
Find the derivative of f(x) = x^3 \sin(x) - \frac{e^x}{x^2} and evaluate f'(\pi).