y=(tan2x)^[cot(x/2)]
lny =cot(x/2) .ln(tan2x)
(1/y) dy/dx = cot(x/2) .[1/(tan2x)]. [ 2(sec2x)^2] + ln(tan2x) . [ -(csc(x/2))^2 ] .(1/2)
= (1/2)cot(x/2) . [1/(sin2x.cos2x) ] -(1/2)ln(tan2x) . [csc(x/2)]^2
dy/dx
= { (1/2)cot(x/2) . [1/(sin2x.cos2x) ] -(1/2)ln(tan2x) . [csc(x/2)]^2 } .(tan2x)^[cot(x/2)]