Question

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

Answer 1

`(dy)/dx = x^{cos(x)} (cos(x)/x - sin(x) log_e x)`

Explanation:

`y = x^{cos(x)} equiv log_e y = cos(x) log_e x`
Deriving the log transformed equation we have
`dy/y = -sin(x)log_e x dx+cos(x)/x dx`
grouping
`(dy)/dx = y(cos(x)/x - sin(x) log_e x)`
and finally
`(dy)/dx = x^{cos(x)} (cos(x)/x - sin(x) log_e x)`