AI engineering glossary · Calculus optimisation
What is derivative?
Derivative: The instantaneous rate of change of a function at a point, defined as the limit of (f(x+h) - f(x)) / h as h shrinks to zero. Geometrically it is the slope of the tangent line. It tells you how much the output moves per tiny nudge of the input.
Derivative: an example
For f(x) = x^2, the derivative is 2x, so at x = 3 the function rises about 6 units per unit step of x.
Related terms
More Calculus optimisation terms
- Derivative-free optimisation
- Differentiability
- Directional derivative
- Duality
- Euler's number
- Exponential function
- Feasible region
- Finite difference
Where you learn it
Derivative is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.