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Amherstclane

Hey there,
First of all, I'm completely new to calculus in any form, so please excuse any completely obvious errors if there are any.
I was just wondering the other day about the derivative of a Power Tower. I tried to treat it as a x^n, and came up with
f(a, b) = a \uparrow \uparrow b
f'(a, b) = (a \uparrow \uparrow b) a^{(a \uparrow \uparrow [b-1]) -1}
Is this correct?
Cheers,
Amherst
(11/14/2009, 05:50 AM)Amherstclane Wrote: [ -> ]Hey there,
First of all, I'm completely new to calculus in any form, so please excuse any completely obvious errors if there are any.
I was just wondering the other day about the derivative of a Power Tower. I tried to treat it as a , and came up with


Is this correct?
Cheers,
Amherst

First a hint: you can enclose your formulas in tex tags like
Code:
[tex]x^n[/tex]
gives the result . I did that for you in the quote.

And then for the derivative: If you have a function with two arguments you must specify with respect to which variable you are differentiating, e.g. .

Before differentiating a whole powertower, let us start with something simpler: What is the derivative of ? You can not simply apply the rule, because this rule is only applicable for being a constant.

If I slightly change the form and write you can see that there are several functions involved of which you know the derivative already:
There is , and there is a product contained , for nested functions you have the chain rule .

So how can you apply all these rules to compute the derivative of ?