November 26, 2015

Homework Help: Calculus - derivatives

Posted by Lucy X on Sunday, November 29, 2009 at 3:58am.

Okay, I want to find the derivative of (x^x)^(x^x)...

Well, I already went through the process of finding the derivative of just x^x (I used ln to do this).
This is what I found...
dy/dx = x^x(lnx+1)

So now I want to find the derivative of (x^x)^(x^x) (using ln).
This is what I did...

y = (x^x)^(x^x)
lny = x^xlnx^x
(1/y)(dy/dx) = (d/dx)(x^x)ln(x^x) + (d/dx)ln(x)^x*(x^x)

Yeah, I don't know if it is right.
Also, how do I find the derivative of ln(x)^x?
It seems simple enough, but I don't know...

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