First of all, replace sinxcosx with 1/2 sin2x. Then you should let U=1/2 Sin2x and replace that in the formula. If y=arctan(U), then U=tany. work out dU/dy which is Sec^{2}y. Using the trigonometric identity sin^{2}y + cos^{2}y= 1, sec^{2}y= 1+tan^{2}y. The differential now becomes 1+U^{2}. Flip the equation around to give dy/dU = 1/(1+U^{2}).to get the differential in terms of y and x first replace U^{2} with 1/4 sin^{2}2x. using chain rule, dy/dx=dy/du * du/dx. du/dx = cos2x, so combining the two equations dy/dx = cos2x/(1 + 1/4 sin^{2}x) which can be simplified to dy/dx = 4cos2x/(4 + sin^{2}2x)