11/14/2009, 08:43 AM

(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]`

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 ?