Find dy/dx for y = x^(x^x) ...using log differentiation?

Limits, differentiation, related rates, integration, trig integrals, etc.
nona.m.nona
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Find dy/dx for y = x^(x^x) ...using log differentiation?

Postby nona.m.nona » Thu Feb 26, 2009 3:34 pm

Find dy/dx for y = xx^x.

ln(y) = ln(xx^x) = xx ln(x)

But then what?

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stapel_eliz
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Postby stapel_eliz » Thu Feb 26, 2009 6:03 pm

nona.m.nona wrote:Find dy/dx for y = xx^x.

ln(y) = ln(xx^x) = xx ln(x)

But then what?

Give it another round of logarithmic differentiation! :wink:

. . . . .

. . . . .

Apply a log rule to get:

. . . . .

. . . . .

Now differentiate:

. . . . .

Simplify, and isolate the dy/dx. Make sure to substitute for "y" and "ln(y)" in the result.

Check my work! :D

nona.m.nona
Posts: 269
Joined: Sun Dec 14, 2008 11:07 pm
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Re: Find dy/dx for y = x^(x^x) ...using log differentiation?

Postby nona.m.nona » Mon Mar 02, 2009 6:49 pm

I finally got it. Thank you!


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