# Interpretation of Derivative

**Slope of the Curve**

The slope of the curve y = f(x) at any point is identical to the derivative of the function dy/dx or y'.

$\text{Slope at any point, } m = y’ = \dfrac{dy}{dx}$

**Rate of Change**

The derivative of a function is identical to its rate of change. Thus, the rate of change of the volume V of a sphere with respect to its radius r is dV/dr.