What is the derivative of $x^(tan x)$ ?

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Answer 1 · 2016-06-26T06:31:32

$y' = x^(tan x)(sec^2 x ln x + tan x/x)$

$y = x^(tan x)$
$ln y = ln x^(tan x) = tanx ln x$
$1/y y' =( tanx ln x)'$

$1/y y' = sec^2 x ln x + tan x (1/x)$ by the product rule

$y' = y(sec^2 x ln x + tan x (1/x))$

$y' = x^(tan x)(sec^2 x ln x + tan x/x)$

What is the derivative of x^(tan x)x^(tan x)?