x^x: derivative where x less than, equal to zero?

[Johnwill]

Hey, i've found out that the derivative of x^x is x^x(lnx+1) where x is greater than 0 but what happens when x is 0 or less than 0?

 

[pka]

Because if we are in the real number field, then we are not allowed to have "even roots" of negative numbers. Therefore, we resrict the domain if the expression x<SUP>x</SUP> to the positive real numbers.