Math
Derivative definition.
Definition
The derivative of a function at a point gives the instantaneous rate of change, or the slope of the tangent line at that point. It is formally defined as the limit of the difference quotient as the interval approaches zero.
Examples
Real-world.
- 1 The derivative of f(x) = x² is f'(x) = 2x, so at x = 3 the slope is 6
- 2 Velocity is the derivative of position with respect to time
- 3 The derivative of a constant function is always 0
Key Fact
f'(x) = lim h→0 [f(x+h) - f(x)] / h