Calculus

Chain Rule - Calculus

Learn the chain rule with examples, step-by-step guide, and calculator tools. Differentiate composite functions

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

The Formula

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

Variables

f(g(x))
Composite function
f'
Derivative of outer function
g'
Derivative of inner function

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 + 1)³] = 3(x² + 1)² × 2x

Example 2

Example 2: 6x(x² + 1)²

Frequently Asked Questions

What is the chain rule?

Differentiate composite functions

How do I calculate chain rule?

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

What tools can help with chain rule?

We provide online calculators: calculator

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