If y= (tan x)^ (tanx)^ (tanx) ^ infinity Prove that dy/dx = (2y^2)(cosec 2x)/ 1 - y log tanx Share with your friends Share 0 Brijendra Pal answered this Hi, We know that ddxlogx = 1x and ddxtanx = sec2xy = tanxtanx...∞y = tanx ytaking log both side, log y = y log tanx since log ax= x log a differentiating wrt y,1y dydx= yddxlog tanx +log tanx ×dydx Using chain rule of differentiationdydx×1y-log tanx = y×1tanx×ddxtanx= ysec2xtanxdydx=y21-ylogtanx×sec2xtanx=y21-ylogtanx×1cos2x×cosxsinx= 2y21-ylogtanx×12sinxcosx = 2y21-ylogtanx×1sin2x= 2y2cosec2x1-ylogtanxsince sin2x=2sinxcosx 1 View Full Answer Ritvik Rohan answered this Hope this helps. -5
