Re: Derivative/Integral of x^x
- From: "steiner@xxxxxxxxxxxxx" <steiner@xxxxxxxxxxxxx>
- Date: 29 May 2006 06:29:17 -0700
G.E. Ivey wrote:
What is the derivative/integral of x^x? I know theyThe derivative of x^x is fairly easy: if y= x^x then
exist, b/c my
graphing calculator can calculate them, but what are
the formulas?
Thanks!!!!!
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!
The integral of x^x is expressible in terms of the Lambda function.
It is not an elementary function.
There have been many posts about this in the past. Suggest you look
through the archives of Sci.math for illuminating discussions.
This question should certainly be added to the FAQ list, IMHO!
Regards,
Ray Steiner
.
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