Computer algebra

Symbolic differentiation

Computing a derivative by applying exact rules to an expression.

Definition

Symbolic differentiation

Symbolic differentiation derives an expression for a function's rate of change.

The algorithm follows rules for sums, products, powers, and compositions. A checker can differentiate independently or verify the local rule applications.

01

Example

The derivative of (x² + 1)³ is 6x(x² + 1)² by the chain rule.

02

Important distinction

A symbolic derivative still depends on the domain and differentiability of the original expression.

After reading this article, you should be able to

  • Define Symbolic differentiation in the sense used on this site.
  • Check a polynomial or composite derivative by applying named rules.