Different custom footnote symbol on the same page

Question

I have redefined the footnote symbol in the preamble as follows:

\renewcommand{\thefootnote}{\color{black}$\spadesuit$}
\newcommand{\txtn}{\textnormal}

Now I have some text, a footnote, and then some more text where I want another footnote, but I want a different symbol (so the reader knows which footnote I'm referring to). How do I redefine the footnote symbol without redefining it globally?

\[(x^a)^{-1} = (\underbrace{x \cdot x \cdot \ldots \cdot x}_{a \txtn{ terms}})^{-1} = \footnote{\tiny By exercise 15.} (x^{-1} \cdot x^{-1} \cdot \ldots \cdot x^{-1})^a = \footnote{different symbol for this footnote} x^{-a}.\]

I expect there to be some kind of command such as \footnote[\symbol]{footnote}.