Question

How do you find the derivative of y=xtan(x)y=x^tan(x)?

Answer 1

$y=x^{\tan x}=e^{\ln x^{\tan x}}=e^{\tan x \ln x}\\ y'=e^{\tan x \ln x}\cdot(\sec^2 x\ln x+\tan x \cdot \frac{1}{x})\\ y'=x^{\tan x}(\sec^2 x\ln x+\frac{\tan x}{x})$

Answer 2

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