How would you differentiate the function $(-1)^x$ w.r.t. $x$. Is the formula for $a^x$ valid here? Wolfram says that the derivative of $(-1)^x$ is $iπ(-1)^x$. So, does this mean than $ln(-1)=iπ$ ?
Another thing that intrigued me was that its domain and range are given to be $\emptyset$. Is it correct?(or does Wolfram Mathematica wants to say that a real domain and range do not exist?)
Update:
There arise 2 cases
1) $f_1 : \mathbb{R} \rightarrow \mathbb{R}$
$f_1(x)=(-1)^x$
2) $f_2 : \mathbb{C} \rightarrow \mathbb{C}$
$f_2(x)=(-1)^x$
Then as per the comments, $f_1$ is not differentiable and its domain and range cannot be specified, while $f_2$ is a differentiable function.(Right?)