Given that y = 4x^3 – 5/(x^2) , x =/= 0, find in its simplest form dy/dx.

We are given: y = 4x^3  – 5/(x^2) To find the dy/dx we are going to use the power rule, from the power rule differentiating x^n gives n*x^n-1, so from our equation differetiating x^3 will give 3x^2, but we need the differential of 4x^3, this will be 12x^3. The derivative of 5/(x^2) is the same as differentiating 5x^-2,  hence, again from the power rule,  differentiating 5x^-2 gives -10x^-3, which is the same as -10/(x^3) so dy/dx = 12x^2 -10/(x^3)