We have studied the notion of average rate of change thus far, for example, change in position over time (velocity), average change in velocity over time (acceleration) etc. However, what if we are interested in finding the instantaneous rate of change of something? To answer this, we will first learn about the concept of the definition of derivative in this section, as well as how to apply it.

Definition of Derivative

$f'\left( x \right) = \;_{h \to 0}^{\;lim}\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}$

$f'\left( x \right) = \;_{h \to 0}^{\;lim}\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}$