1. It is not at all imposible; note that this equals: [tex](x^{x})^{x}=x^{x^{2}}[/tex]
Rewriting this as:
[tex]x^{x^{2}}=e^{x^{2}\ln(x)}[/tex]
We may readily differentate this by means of the chain rule, yielding the derivative:
[tex]x^{x^{2}}(2x\ln(x)+x)[/tex]
2. Please do not re-open nearly 6-year old threads.