If y = (tan x)^(tan x)^(tan x)^....... , then show dy/dx = 2 at x = pie/4

This is a problem of differentiation with infinite series...
well am not getting simply 2 as answer. My answer is 2y^2.

part of my solution is,
let,
y = ( tan x )^y
logy = y log(tan x)
(1/y)dy/dx = y(1/tan x)sec^2x + log(tan x)dy/dx
(1/y)dy/dx = y/(sin x)(cos x)
dy/dx = 2y^2

it should be , dy/dx=2

plzzzz... help

You are almost there:

Now y = tan x so you have dy/dx = 2(tan x)^2

At x = pi/4, tan x = 1.

Substitute to get 2(1)^2 which is equal to 2.