I am using MathJax version 2.x because I want the user to highlight and select a part of a rendered formula, something that is not possible in versions 3.x. The selected part could be changed, so I want to rerender it. The problem is that the formula as a whole could be very big, so the process of rendering it again could turn very slow, and it could be repeated several times. That's why I want to rerender only the selected part.
I know I can change the text of a specific variable with "MathJax.Hub.Queue" and so only rerender it, not the rest, but the problem is that here the whole formula is contained in a single variable. When in the web console I make the query "MathJax.Hub.getAllJax()", I only get one element.
MathJax does not support that ability. Changing one part of a formula may require rerendering other parts of the formula. For example, if you change something inside a square root or a fraction, then the horizontal line for the square root or fraction may need to be wider or shorter, or the size of surrounding parentheses may need to be adjusted. Furthermore, such changes may cause further the need for similar changes to other parts of the expression. So rerendering only a part of an expression without rerendering the rest is not possible, in general.