The derivative gives the rate of change of a [[function]] at any point within its [[domain]]. You can think of this as the slope of the line representing the function on a graph. The notation for a derivative is often expressed as $f'(x)$ or $\frac{dy}{dx}$ to express the rate of change of $x$ with respect to $y$.
The formal definition of a derivative at point $x$ is the [[limit]] as $h$ approaches 0 of the slope of a line between points $x$ and $h$.
$f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$
You can use the definition above to calculate the derivative, but it's much easier to memorize these derivative rules for shortcuts.
- [[derivative of a constant]]
- [[derivative of the sum of functions]]
- [[derivative of an exponential]]
- [[derivative of a log]]
- [[power rule]]
- [[product rule]]
- [[quotient rule]]
- [[chain rule]]