<p align="right">Last Update: <font color="#4f81bd">October, 19, 2024</font></p> #### Definition A derivative is a fancy way of talking about how fast something is changing. It is the slope of a position-time graph or a velocity-time graph. The derivative of x with respect to time is shown below $\frac{dx}{dt}\tag{1}$ This represents the rate of change of $x$ over time ($t$). The specific variable used depends on the context; that is, the letter $x$ may be replaced by any other variable. For example: $\frac{dv}{dt} \tag{2}$ is the rate of change of velocity $v$ with respect to time. This is the definition of acceleration. Multiply the exponent by coefficient then subtract one from the exponent.