To differentiate a simple expression such as x^3 + 2x you simply multiply the power of the x by the multiple in front of the x value and then take away one from the power. For example the expression would become 3x^2+2. The differential is the first derivative of a function and it can represent the gradient of the function. The differential can then be used to find maxima and minima of a function when the differential is equal to zero.