The reason MathJax doesn't do this is that the quotation marks are text-mode effects, and MathJax only does math-mode typesetting.
There are a couple of ways to get your result, however. The first would be to use the actual character you want directly in the input, as in
\frac{d}{dx}\,f(x)\;\text{“is one notation''}
Alternatively, you could use \unicode (outside the \text) to generate the proper character:
\frac{d}{dx}\,f(x)\;\unicode{x201C}\text{is one notation''}
You might notice that both of these don't match the close quote very well. That is because the close quote is actually made from two single quotes, and the spacing between them is slightly different from an actual double quote. So you might try either using the actual character at both ends:
\frac{d}{dx}\,f(x)\;\text{“is one notation”}
or
\frac{d}{dx}\,f(x)\;\unicode{x201C}\text{is one notation}\unicode{x201D}
(or even just the ASCII double quote (") on the right, which has the same glyph), or use two single quotes at the beginning:
\frac{d}{dx}\,f(x)\;\text{‘‘is one notation''}
or
\frac{d}{dx}\,f(x)\;\unicode{x2018}\unicode{x2018}\text{is one notation''}
so that they balance better.
It would be possible to write an extension that handles the `` notation, but I'm not sure if this is something that you need a lot or just for special cases, so I didn't work that out. There are several possible approaches.
Davide