What is differentiation and how is it used?

Differentiation is a branch of calculus mathematics used to determine the rate of change between certain variables. For example if an object changes its distance x over a certain time interval t, we can use differentiation to determine the rate of change of distance with respect to time (dx/dt), otherwise known as the velocity of the object. The phrase 'with respect to' just means that one variable is changing relative to another i.e. with respect to another. Graphically, differentiation is used to determine the gradient of a line which can be plotted between two variables. Using the same example as before, we can calcuate the gradient of the line at any point in time to work out its instantaneous velocity at that point.