Question

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

Answer 1

`d/dxx^(ln x) = 2x^(ln x-1) ln x`

Explanation:

Let `y = x^(ln x)`
Taking the natural logarithm:
`ln y = (ln x)^2`

Taking the derivative with respect to x:
`1/y dy/dx = (2ln x)/x`
`dy/dx = 2x^(ln x-1) ln x`