Derivatives: The Basics
The mathematical description of an instantaneous rate of change.
Definition of the Derivative
The derivative of $f(x)$ at a point measures its instantaneous rate of change, defined as a limit:
$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$Basic Derivative Rules
| Function | Derivative |
|---|---|
| $x^n$ | $nx^{n-1}$ |
| $\sin x$ | $\cos x$ |
| $\cos x$ | $-\sin x$ |
| constant $c$ | $0$ |
Lesson 23 of 27