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.
 

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