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y-tan-x-tan-x-tan-x-




Question Number 19199 by priyankavarma094@gmail.com last updated on 06/Aug/17
y=tan x^(tan x^(tan x) )
y=tanxtanxtanx
Answered by NEC last updated on 06/Aug/17
let u=tan x    y=u^u^u    ln y=u^u ln u  (1/y)dy/dx=u^u ((1/u))+(u^u +ln u)ln u    (dy/dx)=y[(u^u .(1/u) + (u^u +ln u)ln u)]  (dy/dx)=tanx^(tanx^(tanx ) ) {(tanx^(tan x−1)  +(tanx^(tanx ) +ln tan x)ln tan x)}
letu=tanxy=uuulny=uulnu1ydy/dx=uu(1u)+(uu+lnu)lnudydx=y[(uu.1u+(uu+lnu)lnu)]dydx=tanxtanxtanx{(tanxtanx1+(tanxtanx+lntanx)lntanx)}
Commented by NEC last updated on 06/Aug/17
thats if you needed (dy/dx)
thatsifyouneededdydx

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