Question

x = 2cost - cos2t and y = 2sint - sin2t Derivative of higher order

Answer 1

i think the answer is sin

Answer 2

dx/dt=-2sint+2sin2tdy/dt=2cost-2cos2tdy/dx=(dy/dt)/(dx/dt)=(cost-cos2t)/(-sint+sin2t)dy/dx=2sin3t/2.sint/2/2cos3t/2sint/2=tan3t/2d2y/dx2=d/dx(dy/dx)=d/dt(dy/dx).dt/dx=(3/2).sec23t/2.1/(-2sint+2sin2t)=3/4.1/cos2(3t/2).1/(sin2t-sint)=3/4.1/cos2(3t/2).1/2cos3t/2.sint/2=(3/8).1/(cos33t/2.sint/2put t= pi/2d2y/dx2=3/8. 1/(cos3(3pi/4).sin(pi/4))=-3/2Thanks & RegardsRinkoo GuptaAskIITians Faculty