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October 30th, 2008, 05:28 PM   #1
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tangent to x^x

the problem is

find tangent line to x^x that passes through origo.

i didnt get far:

y=x^x
lny=x*lnx
y=e^(x*lnx)

dy/dx = e^(x*lnx)*(x*1/x +lnx) = x^x(lnx +1) (is this derivative correct?)

so, dy/dk must equal the slope of the line that passes though origo and so has equation y = (dy/dx)*x

and im pretty much stuck here.

Any help much appreciated!
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October 30th, 2008, 06:05 PM   #2
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Re: tangent to x^x

Differentiate in the second line implicitly.

y=x^x, so ln(y) = xln(x) <-----Here.

Then separate variables and sub back for y.

Too many late nights and I'm too tired to go on.
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November 2nd, 2008, 01:16 PM   #3
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