Application of Derivatives to Physical Systems:

There are several different problems involving dynamic physical systems which are most readily solved using derivatives. One  of  the  best  description  of  the  application  of  derivatives  are problems involving associated rates of change. While two quantities are associated by some known physical relationship, those rates of change with respect to a third quantity are also related.  For instance, the area of a circle is associated to its radius through the formula A =r².  If for some purpose the size of a circle is changing within time then the rate of change of its area, along with respect to time for example, is also associated to the rate of change of its radius along with respect to time.  Although these applications include searching the derivative of function, they described why derivatives are required to solve certain problems including dynamic systems.