Given that y= x^(-3/2) + (1/2)x^4 + 2, Find: (a) the integral of y (b) the second differential of y

This is a typical question for a Core 1 paper. (a) integral of y = (-2)x^(-1/2) + 0.1x^5 + 2x +C Method: Increase the power of x by +1, divide the term through by the new power. (b) dy/dx = (-3/2)x^(-5/2) + 2x^3 + 2 d2y/dx2 = (15/4)x^(-7/2) + 6x^2 Method: Multiply the coefficient of x by its power, then reduce the power of x by 1. This process is completed twice in order to reach the second differential.