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seen Jun 18 at 13:49

Apr
29
awarded  Scholar
Apr
29
accepted Generalized power rule for derivatives
Apr
29
awarded  Commentator
Apr
29
comment Generalized power rule for derivatives
Other than for $f=0$, are there well defined functions $f(x)^{g(x)}$ for which your modified general rule doesn't work?
Apr
29
revised Generalized power rule for derivatives
fixed the cases I care about
Apr
29
awarded  Supporter
Apr
29
comment Derivative of $f(x)^{g(x)}$ at points when $f(x)=0$
Why do you specify even constants $c$? Isn't $f^c$ well defined for all integer constants $c$?
Apr
28
awarded  Editor
Apr
28
revised Generalized power rule for derivatives
Clarified my exact question
Apr
28
comment Generalized power rule for derivatives
@NotNotLogical This is correct. Ill update the question to make that more clear
Apr
28
comment Generalized power rule for derivatives
@Hagen Hmm... I see the problem here. I don't actually care about that case, but I don't really have a good way to tell which case I'm dealing with. I was hoping that there would be some general rule, but I guess Ill have to figure out how to tell what case I'm in, as fgp said.
Apr
28
comment Generalized power rule for derivatives
@Hagen Is that a useful distinction? What is the application of square root if not solving equations? Also, how is that different from the case outlined here, the way it is worded now is "E.g., $y^n=x$ has $n$ solutions in $\mathbb C$" (I'm pointing out the word "solutions" here)
Apr
28
comment Generalized power rule for derivatives
Aren't square roots already non-unique? i.e. $\sqrt{4}=\pm 2$?
Apr
28
comment Generalized power rule for derivatives
Also, I don't actually care about that case
Apr
28
comment Generalized power rule for derivatives
It seems like people are having issues with exponentiation of negative numbers. I'm not really sure how those are usually evaluated, but I can tell you what some of them are. For example: $(-5)^{1/2}=5i$ Other than that, I fear I don't understand what you are asking.
Apr
28
comment Generalized power rule for derivatives
@Hagen Well, I'm talking about derivatives, so if you have defined $f(x)=-1.234$ and $g(x)=4.567$ where $F(x)=f^g$ then $F^\prime(x)=0$
Apr
28
comment Generalized power rule for derivatives
@Hagen I don't understand the question. It looks like you have defined it there. That is one of the cases I don't care about.
Apr
28
awarded  Student
Apr
28
asked Generalized power rule for derivatives