One of the main branches of calculus, counterpart to integration. The core idea is that we measure rate of change.

Interpretation

For some function :

  • , then is increasing
  • , then is decreasing
  • , then is concave up
  • , then is concave down

Key concepts

Foundations

Applications

Computer methods

The Symbolic Math Toolbox has a differentiation command, which works with functions of multiple variables:

syms x;
y = x^2 + x;
diff(y, x) % second input is variable to take derivative wrt

Useful rules

For , we use the product rule:

For , we use the quotient rule:

For some and ) we use the chain rule:

Standard derivatives

See inverse differentiation for a derivation of the derivatives of inverse trigonometric functions.