# JEE Main & Advanced Mathematics Differentiation Derivative as the Rate of Change

## Derivative as the Rate of Change

Category : JEE Main & Advanced

If a variable quantity $y$ is some function of time $t$ i.e., $y=f(t),$ then for a small change in time $\Delta t$ we have a corresponding change $\Delta y$ in $y$. Thus, the average rate of change $=\frac{\Delta y}{\Delta t}$. The differential coefficient of $y$ with respect to $x$ i.e., $\frac{dy}{dx}$ is nothing but the rate of change of $y$ relative to $x$.

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