when differentiating, we multiply the power by the coefficient and then take the power away by 1 so : y= 4x^3 + 3x^2 -5x +1 then 4 x 3= 12 and 3-1 = 2 meaning the solution is 12x^2. 2 x 3 = 6 and 2-1 = 1 giving a solution of 6x. 1x.-5= -5 amd 1-1= 0 so the x value dissapears as x^0 = 1 and finally the 1 does not have a variable so it can't be differentiated so it is excluded. so dy/dx= 12x^2 + 6x -5