Question

How do you find the derivative of `y = x^(ln x)`?

Answer 1

Rewrite as: `y = e^ln(x^lnx) = e^(lnxlnx) = e^((lnx)^2)`

Explanation:

Now differentiate using the chain rule

`dy/dx = e^((lnx)^2)[2(lnx)(1/x)]`

`= (2lnx)/x x^lnx`