Question

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

Answer 1

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

Explanation:

`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)`