A derivative measures the **instantaneous rate of change** of a function — how fast the output is changing at a specific point.
**Intuition:** Imagine driving a car. Your position changes over time. The derivative of your position is your **speed** (velocity). The derivative of your speed is your **acceleration**.
Formally: the derivative f'(x) is the slope of the tangent line to f(x) at point x.
``` f'(x) = lim(h→0) [f(x+h) - f(x)] / h ```
**Common derivatives:** - d/dx(xⁿ) = nxⁿ⁻¹ (power rule) - d/dx(eˣ) = eˣ - d/dx(sin x) = cos x - d/dx(ln x) = 1/x
**Example:** f(x) = x² → f'(x) = 2x. At x=3, the slope is 6.