Differentiation

Calculus is an extension of analytic geometry which deals with continuously varying quantities. Differentiation is the process of finding out how quickly a quantity changes, and here, the rate of change is obtained. Below diagram represents a customer shopping in a supermarket. The position from start to point of stopping in a specific aisle number is changing continuously  At any given time, t, its position, x is represented by the continuous function x(t). The shopping trolley continues to move, and after increment of time, this will change to become x + ux. The shopping trolley arrives into aisle number 12 at its new position in time, which will be the sum of the original time, t and the total amount traveled (t + Ut).