What is Derivative?

It is defined as a limit, $f'(x) = \lim_{h \to 0}\dfrac{f(x+h) - f(x)}{h}$. Useful rules: $\dfrac{d}{dx}x^n = nx^{n-1}$, $\dfrac{d}{dx}\sin x = \cos x$, $\dfrac{d}{dx}e^x = e^x$. At a maximum or minimum of a smooth function the derivative is zero. In physics, velocity is the derivative of position and acceleration is the derivative of velocity.