Answer :
[tex]y=x^{\tan x}=e^{\ln x^{\tan x}}=e^{\tan x \ln x}\\
y'=e^{\tan x \ln x}\cdot(\sec^2 x\ln x+\tan x \cdot \frac{1}{x})\\
y'=x^{\tan x}(\sec^2 x\ln x+\frac{\tan x}{x})\\[/tex]
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