What is differentiation

Differentiation is a mathematical operation which we can use to study how one quantity, such as the distance travelled by a train, is affected by another quantity, such as time. For example, if the train is travelling at a constant speed, the distance travelled by the train increases linearly with time. Differentiation is also closely related to the gradient of a line on a graph, since it can be shown that the derivative of a line is simply its gradient. So, if we now plot the distance travelled by the train with respect to time in the situation just given, we draw a straight line where distance increased with time. The derivative of this line gives the gradient, and because this line is straight, therefore it’s gradient is constant, and the derivative is constant. It is no coincident that this whole scenario arose by supposing that the train is travelling at a constant speed, because speed is in fact the derivative of distance with respect to time.