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Product Rule

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

Description

Finds the derivative of a product of two functions.

Variables

Symbol Meaning
f(x) First function
g(x) Second function
f'(x) Derivative of first function
g'(x) Derivative of second function

Example

Problem

Find d/dx[x²·sin(x)]

Solution

2x·sin(x) + x²·cos(x)

Real-World Applications

  • Physics
  • Engineering
  • Economics