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Trouble to find answer - Amherstclane - 11/14/2009
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 Derivative of powertower - bo198214 - 11/14/2009
(11/14/2009, 05:50 AM)Amherstclane Wrote: Hey there, 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 ? |