What is the definition of the derivative of a function and what does it represent?

The formula shown is:

This formula defines the derivative $\frac{df}{dt}$ as the instantaneous rate of change of the quantity $f$ with respect to time $t$. It is calculated as the limit of the average rate of change, $\frac{\text{change in } f}{\text{time interval } h}$, as the time interval $h$ tends to zero (becomes infinitesimally small).