# What is meant by the term differentiation?

A good example of this is the position-time function $x \left(t\right)$ as when you differentiate this function you will be able to to know the value of the instantaneous velocity $\frac{\mathrm{dx}}{\mathrm{dt}}$ at a given time $t$ and same goes for the velocity-time function $v \left(t\right)$ as you will be able to calculate the value of the instantaneous acceleration $\frac{\mathrm{dv}}{\mathrm{dt}}$ at a given time $t$
Also, it's used to calculate the slope of a non-linear equation as $y = {x}^{3}$ as the slope depends on $x$ and not a constant like in linear equations as $y = m x + c$ in which the slope will be equal to $m$