Chain Rule

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

Description

Finds the derivative of composite functions.

Variables

Symbol Meaning
f(x) Outer function
g(x) Inner function
f' Derivative of outer function
g'(x) Derivative of inner function

Example

Problem

Find d/dx[(2x+1)³]

Solution

3(2x+1)² · 2 = 6(2x+1)²

Real-World Applications

  • Physics
  • Engineering
  • Optimization