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Differentiating y = x^x


From: Antill J M
Date: Thu, 3 Nov 94 17:44:02 GMT
Subject: Problem

Please could you differentiate

y=X^X
that's X to the power of X

From: Dr. Ken
Date: Thu, 3 Nov 1994 12:58:23 -0500 (EST)

Hello!

In problems like these, where the variable is in an exponent, try rewriting
the problem as y = e^(log(x^x)).  That's

                      x
                 log(x )
            y = e        .

Then you can use the properties of logarithms and the product rule to
differentiate more easily.

-Ken

Associated Topics:
High School Calculus

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