Derivative of X^(x^x)?

[appplejack]

Homework Statement

I uploaded a image file of the question.

Homework Equations

I've seen the derivative of X^x but how do I do this one?

The Attempt at a Solution

 

[rock.freak667]

Put t=x^x and apply the chain rule since you know what d/dx(xsup]x[/sup]) gives.