d/dx((15 x^3-120 x^2+500 x+750)/x) (15 x^3-120 x^2+500 x+750)/x = (750+500 x-120 x^2+15 x^3)/x: = d/dx((750+500 x-120 x^2+15 x^3)/x) = (-(750+500 x-120 x^2+15 x^3) (d/dx(x))+x (d/dx(750+500 x-120 x^2+15 x^3)))/x^2 = (x (d/dx(750+500 x-120 x^2+15 x^3))-1 (750+500 x-120 x^2+15 x^3))/x^2 = (-750-500 x+120 x^2-15 x^3+x (d/dx(750+500 x-120 x^2+15 x^3)))/x^2 = (-750-500 x+120 x^2-15 x^3+d/dx(750)+500 d/dx(x)-120 d/dx(x^2)+15 d/dx(x^3) x)/x^2 = (-750-500 x+120 x^2-15 x^3+x (500 (d/dx(x))-120 (d/dx(x^2))+15 (d/dx(x^3))+0))/x^2 = (-750-500 x+120 x^2-15 x^3+x (500 (d/dx(x))-120 (d/dx(x^2))+15 (d/dx(x^3))))/x^2 = (-750-500 x+120 x^2-15 x^3+x (-120 (d/dx(x^2))+15 (d/dx(x^3))+1 500))/x^2 = (-750-500 x+120 x^2-15 x^3+x (500+15 (d/dx(x^3))-120 2 x))/x^2 = (-750-500 x+120 x^2-15 x^3+x (500-240 x+15 (d/dx(x^3))))/x^2 = (-750-500 x+120 x^2-15 x^3+x (500-240 x+15 3 x^2))/x^2 = (-750-500 x+120 x^2-15 x^3+x (500-240 x+45 x^2))/x^2 = (-750-500 x+120 x^2-15 x^3+ 500 x-240 x^2+45 x^3)/x^2 = (-750-120 x^2+30 x^3)/x^2 = 30(-25-4 x^2+ x^3)/x^2