`"If "y=(tan x)^((tan x)^(tan x))," then find "(dy)/(dx).`

1.	`"If "y=(tan x)^((tan x)^(tan x))," then find "(dy)/(dx).`
Answer» Correct Answer - `y log y sec^(2)x[log tan x + 1 +(1)/(tan x log tan x)]` Taking logarithm on both sides, we get `log y = (tan x)^(tan x)log tan x` `therefore" "log log y = [ tan x log tan x ] + log log tan x ` Differentiating w.r.t x, we get `(1)/(y log y )(dy)/(dx)=sec^(2) x log tan x + tan x (sec^(2)x)/(tan x)+(1)/(log tan x )xx(sec^(2)x)/(tan x)` `therefore" "(dy)/(dx)=y log y sec^(2) x [ log tan x + 1+ //(tan x log tan x )]`

Discussion

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