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# differentiate x^x? watch

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1. How do I differentiate: x^x?

Thank you,
H2O
2. Notice that xx = elog(xx) = ex logx

Go from there.
3. (Original post by [email protected])
How do I differentiate: x^x?

Thank you,
H2O
Let y = x^x
=> lny = xlnx
=> (1/y).dy/dx = x.(1/x) + lnx = 1 + lnx
=> dy/dx = y(lnx + 1)
=> dy/dx = x^x(lnx + 1)
=> d/dx[x^x] = x^x(lnx + 1)

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Updated: November 15, 2005
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