Derivative
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
- Derivative
Has many definitions:
- The rate of change in one variable with respect to another at a single instant
- Slope of a tangent line
- How a function responds to very small changes in its input
Notation examples: , , , , , ,
- Related Glossary Terms
Derivative of an Inverse, Implicit differentiation, Limit, Mean Value Theorem, Newton-Raphson Method, Power rule, Product Rule, Quotient rule, Reciprocal rule, Rolle’s Theorem, Second Derivative
- Index
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
-
Derivative
A derivative gives the instantaneous rate of change of a function with respect to its input. At a point, it is the finite limit of the difference quotient when that limit exists. For example, the derivative of x² is 2x, so the tangent slope at x=3 is 6. A derivative function collects those rates across the inputs where the function is differentiable.