Can someone help me to derivatex^x^x? I'm starting to belive it's not possible... : D heeelp! :) Thank you in advance!

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- January 24th 2007, 06:20 AMkukkeballTricky derivation...
Can someone help me to derivate

**x^x^x**? I'm starting to belive it's not possible... : D heeelp! :) Thank you in advance! - January 24th 2007, 06:42 AMearboth
- January 24th 2007, 06:49 AMAfterShock
Oh, it's perfectly possible, and fun too ;) .

I have class soon, but I will get you started.

First, what is the derivative of x^x?

We have y = x^x

Note: x > 0

ln(y) = ln(x^x)

ln(y) = x*(ln(x))

Differentiate both sides with respect to x;

y'(1/y) = ln(x) + x*(1/x) = (ln(x) + 1)

y' = (ln(x) + 1)*y

But recall y = x^x

y' = (ln(x) + 1)*x^x

Now you can use this to find the derivative of x^x^x. - January 24th 2007, 07:13 AMAfterShock
- January 24th 2007, 11:48 AMearboth
- January 25th 2007, 09:54 AMkukkeball
So what's the correct answer... i got something crazy... : F

- January 25th 2007, 12:34 PMSoroban
Hello, kukkeball!

Here's another approach . . .

Quote:

Differentiate: .

Take logs: .

Take logs again: .

Differentiate implicitly (**very**carefully) . . .

. .

We have: .

Then: .

Therefore: .