Re: Derivative/Integral of x^x

What is the derivative/integral of x^x? I know they
exist, b/c my
graphing calculator can calculate them, but what are
the formulas?
Thanks!!!!!

The derivative of x^x is fairly easy: if y= x^x then
ln(y)= xln(x). The derivative of log(y) with respect to x, by the chain rule, is (1/y)(dy/dx) and the derivative of xln(x), by the product rule, is ln(x)+ x(1/x)= ln(x)+ 1. That is, (1/y)(dy/dx)= ln(x)+ 1 and so dy/dx= y(ln(x)+ 1)= x^x ln(x)+ x^x.

I would be interested in knowing what your calculator gives for the integral of x^x!
.