If `pi/2 lt x lt pi`, then find `d/dx(sqrt((1+cos2x)/2))`

Find d/(dx)(1/(sqrt(1-x^2))

If pi lt x lt 2 pi , then (d)/(dx) [ tan ^(-1) ((1 - cos x)/( 1 + cos x))^(1//2) ] is . . . .

Comprehension 2 (Q.No 4 to 6) It is known that sqrt(tanx)+sqrt(cotx)={{:(sqrt(sinx)/sqrt(cosx)+sqrt(cosx)/sqrt(sinx), if 0ltxltpi/2),(sqrt(-sinx)/sqrt(cosx)+sqrt(-cosx)/sqrt(-sinx),if pi lt x lt (3pi)/(2)):} d/(dx)(sqrt(tanx)-sqrt(cotx)) =1/2(sqrt(tanx)+sqrt(cotx))(tanx+cotx), AA in (0,pi,2) uu (pi,(3pi)/2) and d/(dx)(sqrt(tanx)+sqrt(cotx))=1/2(sqrt(tanx)-sqrt(cotx))(tanx+cotx), AA x in (0,pi/2) uu (pi, (3pi)/(2)) . Value of the integral I=int(sqrt(tanx)+sqrt(cotx)) dx, where x in (0,pi/2) , is

Find by the definition the differential coefficient of the following: If y=sqrt((1-cos2x)/(1+cos2x)) xin(0,pi/2) cap (pi/2 , pi) then find dy/dx

[(d)/(dx)[log sqrt((1-cos2x)/(1+cos2x))]

(d)/(dx)[cos^(-1)sqrt(((1+x))/(2))]

differentiate the following functions wrt x,sqrt((1-cos2x)/(1+cos2x))

Differentiate w.r.t x the function 0 lt x lt (pi)/(2), cot^(-1) [(sqrt(1 + sin x) + sqrt(1-sin x))/(sqrt(1+ sin x)-sqrt(1-sin x))]