Calculus and change
Derivative
The instantaneous rate of change of a function, defined as a limit of average rates where that limit exists.
In one sentence
What does Derivative mean?
The instantaneous rate of change of a function, defined as a limit of average rates where that limit exists.
How it is written
f′(x) = lim[h→0] (f(x+h)−f(x))/h
A compact example
If f(x)=x², then f′(x)=2x.
Other names and search terms
differentiation, rate of change.
Where this fits
When should you learn Derivative?
The first encounter is not the final level. Many ideas begin visually, become computational in high school and become formal in college.
- 1Pre-high schoolPrepare foundations
- 2High schoolUsually introduced
- 3CollegeGreater depth
- 4AdvancedGreater depth
- Calculus
- Differential equations
- Functions
- Algebra
- Trigonometry
- Continuous models
- Wave equations
- Optimisation
Derivatives and integrals describe evolution, waves and measurable quantities.
Open the Zero-to-QM pathClear answers
Questions about Derivative
What does Derivative mean in mathematics?
The instantaneous rate of change of a function, defined as a limit of average rates where that limit exists.
How is Derivative written?
A common notation is f′(x) = lim[h→0] (f(x+h)−f(x))/h.
What is an example of Derivative?
If f(x)=x², then f′(x)=2x.