"Missing '{' inserted" and "Missing } inserted" with aligned environment

Question

I'm trying to write something out some math in LaTeX with two aligned columns using the aligned environment, which seems to have the best results so far. Using the following code, I have no issue, and it comes out pretty much exactly as I want it to:

\[
    \begin{aligned}[c]
        f(x) &= e^{-4x}\\
        f'(x) &= -4e^{-4x}
    \end{aligned}
    \qquad
    \begin{aligned}[c]
        f(0) &= e^0 = 1\\
        f'(0) &= -4e^0 = -4
    \end{aligned}
\]

But I'll be doing this a lot in the document I'm working on, so I want to make this a command. The code I use for the command is

\newcommand{\mtable}[2]{
    \[
        \begin{aligned}[c]
            {#1}
        \end{aligned}
        \qquad
        \begin{aligned}[c]
            {#2}
        \end{aligned}
    \] 
    }

but now when I try to use this command in the same way, like so

\mtable{
    f(x) &= e^{-4x}\\
    f'(x) &= -4e^{-4x}
}{
    f(0) &= e^0 = 0\\
    f'(0) &= -4e^0 = -4
}

I get two errors that say Missing { Inserted. and two errors that say Missing } inserted. all pointing to the last line in the previous block of code. As far as I can tell, there's no unmatched parentheses, and I've tried removing the parentheses around {#1} and {#2} from the command definition but nothing has quite worked, so I'm not sure what's wrong with this code.

Forgive me if this is a duplicate question, but for most other similar questions I've found, the answer has been that there was an incorrect \left or \right, and I don't think that applies in my case.

Edit: Playing around with it some more, I've found that the issue seems to be the newline command (\\). When I remove it, I don't get the error, but obviously I also don't get new lines where I need them.

Answer 1

Drop your use of braces around the arguments #1 and #2 in your \mtable definition:

\documentclass{article}

\usepackage{amsmath}

\newcommand{\mtable}[2]{%
  \[
    \begin{aligned}[c]
      #1
    \end{aligned}
    \qquad
    \begin{aligned}[c]
      #2
    \end{aligned}
  \] 
}

\begin{document}

\mtable{
  f(x)  &=   e^{-4x} \\
  f'(x) &= -4e^{-4x}
}{
  f(0)  &=   e^0 =  0 \\
  f'(0) &= -4e^0 = -4
}

\end{document}

The braces are split across & and \\ when placed inside the aligned environment, and this cannot be done.