y=(tanx)power(tanx)power(tanx).........infinity.

prove that  dy/dx =2  if   x=pie/4.

 c rite it as y=(tanx )^y

nw u can diff it easily

dy/dx=tanx^(y)*[ylog tanx]

dy/dx=tanx^(y)*(dy/dxlog tanx+ysec^2x/tanx)

thus u get dy/dx=2

ans) put y=(tanx)power(tanx)power(tanx).........infinity.



now by diff v get 

dy/dx=tanx^y X [log tanx]

dy/dx=tanx^y X [dy/dxlog( tanx)+ysec²x/tanx]

now put  x=pie/4 u get dy/dx = 2

i think this might help u

y = tanx ^{tanx -------------infi}

y = tanx ^y

taking log

log y = y log tanx

differentiating

( 1/ y )dy / dx  = y [ ( 1/ tanx )*sec²x ] + log tanx ( dy/ dx)

so,

dy / dx { [ 1 / y ] - log tanx } =y [ ( 1/ tanx )*sec²x ]

putting x = pi/4

y=1

so dy / dx = 2

plz rate