How do I push the tag to my custom environment equation to be flush right?

Question

The tag for the custom environment housing an equation is not placing the tag flush right. I may not have the right search terms because I am not finding the solution for this issue. Here is my MWE:

\documentclass{article}

\usepackage{mathtools}

% PRB: Tag placement on a line does not position flush right.
\newcounter{derivativeFormula}
\renewcommand*{\thederivativeFormula}{\textsc{df}\arabic{derivativeFormula}}
\usepackage{zref-savepos}
\makeatletter
\newenvironment{DerivativeFormula}{                               %
    \def\equation{$$\refstepcounter{derivativeFormula}}           % order
    \def\@eqnnum{{\normalfont \normalcolor \thederivativeFormula}}% is
    \equation                                                     % important!
}{                                                                %
    \@gobble                                                      %
    \print@eqnum{(\thederivativeFormula)}                         %
    \endequation                                                  %
}
\makeatother

\begin{document}

A regular equation which should be reference (1).
\begin{equation}\label{eqn:testA}
  \frac{dx}{dx} = 1
\end{equation}

A regular equation which should be reference (2).
\begin{equation}\label{eqn:testB}
  \frac{d(u+v)}{dx} = \frac{du}{dx}+\frac{dv}{dx}
\end{equation}

This is the \texttt{DerivativeFormula} environment. I want the tag 
to be flush right. It should read (DF1) but way that way -->.
\begin{DerivativeFormula}\label{eqn:testC}
  \frac{d(uv)}{dx} = u\frac{du}{dx} + v\frac{du}{dx}
\end{DerivativeFormula}

Another plain equation to check numbering and reference (3).
\begin{equation}\label{eqn:testD}
  \frac{du^n}{dx} = nu^{n-1}\frac{du}{dx}
\end{equation}

The values of the references are, in order, 
\eqref{eqn:testA}, \eqref{eqn:testB}, \eqref{eqn:testC}, \eqref{eqn:testD}.

\end{document}

Answer 1

The key is to use \tag, Barbara reminds me that \tag works inside of equation when amsmath (or mathtools) is loaded, thus I EDITED to replace my choice of gather with the equation environment.

\documentclass{article}

\usepackage{mathtools}

\newcounter{derivativeFormula}
\renewcommand*{\thederivativeFormula}{\textsc{df}\arabic{derivativeFormula}}
\usepackage{zref-savepos}
\makeatletter
\newenvironment{DerivativeFormula}{
    \refstepcounter{derivativeFormula}
    \equation
}{
    \tag{\thederivativeFormula}
    \endequation
}
\makeatother
\begin{document}
A regular equation which should be reference (1).
\begin{equation}\label{eqn:testA}
  \frac{dx}{dx} = 1
\end{equation}

A regular equation which should be reference (2).
\begin{equation}\label{eqn:testB}
  \frac{d(u+v)}{dx} = \frac{du}{dx}+\frac{dv}{dx}
\end{equation}

This is the \texttt{DerivativeFormula} environment. I want the tag 
to be flush right. It should read (DF1) but way that way $\rightarrow$.
\begin{DerivativeFormula}\label{eqn:testC}
  \frac{d(uv)}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}
\end{DerivativeFormula}

Another plain equation to check numbering and reference (3).
\begin{equation}\label{eqn:testD}
  \frac{du^n}{dx} = nu^{n-1}\frac{du}{dx}
\end{equation}

The values of the references are, in order, 
\eqref{eqn:testA}, \eqref{eqn:testB}, \eqref{eqn:testC}, \eqref{eqn:testD}.
Here is the next derivative formula:
\begin{DerivativeFormula}\label{eqn:testZ}
  \frac{d(uw)}{dx} = u\frac{dw}{dx} + w\frac{du}{dx}
\end{DerivativeFormula}
\end{document}

p.s. I also corrected the math in (DF1).