Using a Suitable substitution or otherwise, find the differential of y= arctan(sinxcosx), in terms of y and x.

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 Sec2y. Using the trigonometric identity sin2y + cos2y= 1, sec2y= 1+tan2y. The differential now becomes 1+U2. Flip the equation around to give dy/dU = 1/(1+U2).to get the differential in terms of y and x first replace U2 with 1/4 sin22x. using chain rule, dy/dx=dy/du * du/dx. du/dx = cos2x, so combining the two equations dy/dx = cos2x/(1 + 1/4 sin2x) which can be simplified to dy/dx = 4cos2x/(4 + sin22x)

Related Further Mathematics A Level answers

All answers ▸

Find the volume of revolution formed by rotating the curve y = sinx 2pie around the x- axis


'Find the first derivative, with respect to x, of arctan(1/x) for non-zero real x. Hence show that the value of arctan(x)+arctan(1/x) is constant for all non-zero x, explicitly stating this constant in your final answer.' How do I solve this?


Given a curve with parametric equations, x=acos^3(t) and y=asin^3(t), find the length of the curve between points A and B, where t=0 and t=2pi respectively.


f(x) = 9x^3 – 33x^2 –55x – 25. Given that x = 5 is a solution of the equation f(x) = 0, use an algebraic method to solve f(x) = 0 completely.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences