Calculus

Product Rule - Calculus

Learn the product rule with examples, step-by-step guide, and calculator tools. Differentiate product of two functions

The product rule is a fundamental concept in calculus. Differentiate product of two functions. This page provides a comprehensive guide with worked examples and practical applications.

The Formula

\[\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)\]

Variables

f(x), g(x)
Functions
f'(x), g'(x)
Derivatives

Step-by-Step Guide

  1. 1

    Step 1: Gather your data values

  2. 2

    Step 2: Apply the formula

  3. 3

    Step 3: Perform the calculations

  4. 4

    Step 4: Interpret the result

Examples

Example 1

Example 1: [] → d/dx[x² × sin(x)] = 2x × sin(x) + x² × cos(x)

Example 2

Example 2: 2x sin(x) + x² cos(x)

Frequently Asked Questions

What is the product rule?

Differentiate product of two functions

How do I calculate product rule?

Use the formula: \frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x). Follow the steps provided above.

What tools can help with product rule?

We provide online calculators: calculator

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