How do you differentiate a function?

The differential of a function is defined by the expression: dy/dx = Lim(dx->0) of (f(x+dx)-f(x))/dx. For functions only involving powers of x, the differentioal can easily be calculated by timesing by the power, and then reducing the power by 1. For example: y = f(x) = 3x² The differential, dy/dx, is: dy/dx = 6x, where here the coefficient, 3, is multoplied by the power, 2 to give 6, and the power is reduced by 1 to give a power of 1.