Question

How do you differentiate `f(x)=x^(ln x)`?

Answer 1

See the explanation section, below.

Explanation:

`y=x^(lnx)` `rArr` `lny = lnx^(lnx) = lnx lnx = (lnx)^2`

Differentiate implicitely:

`1/y dy/dx = 2(lnx)* 1/x`

So, `dy/dx = y(2lnx)/x = (2lnx)/x x^(lnx)`