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
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 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