Interactive: Derivative of a Function

Derivative of a Function at $a$, if it exists:

$$f'\left( a \right) = \mathop {\lim }\limits_{h \to 0} \frac{{f\left( {a + h} \right) - f\left( a \right)}}{h}$$

Instructions: Drag the green dot representing a+h toward a to simulate h tending toward zero.