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
- Differentiation from first principles
- Differentiability
- Implicit differentiation
- Partial differentiation
- Fundamental theorem of calculus
- Chain rule
Applications
Computer methods
The Symbolic Math Toolbox has a differentiation command, which works with functions of multiple variables:
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.