Parentheses changing size depending on what's in them?

Question

Very simple problem, but very confusing. When I type

\left( \frac{\partial f}{\partial x }  \right)^2

I get smaller parentheses but when I type the same thing but with y instead of x, i.e.

\left( \frac{\partial f}{\partial y }  \right)^2

I get larger ones... what's up with that? Is it a known problem or do I have to supply more information?

UPDATE (after reading some comments):

This difference isn't present if the expression is written by itself, but only if it's in the denominator, i.e. when I write

\frac{...something...} { \left( \frac{\partial f}{\partial x }  \right)^2 + \left( \frac{\partial f}{\partial y}  \right)^2}

I get parentheses of different size!

Answer 1

Here is an great old post that provide thorough explanation on how \left and \right work:

Incorrect delimiter size in math mode

Now back to your question, as karlkoeller explained, letter y adds more vertical space so the parenthesis become bigger. It can be observed as the following

There are basically three ways to solve the problem, we can choose among redefining \left and \right (which is strongly recommended) as the post above suggested, increase the size of df/dx, and decrease the size of df/dy. The size changing can be accomplished by using \rule or \raisebox:

\documentclass{article}
\usepackage{amsmath}

\newlength{\dyfoo}
\newlength{\hyfoo}
\newlength{\dxfoo}
\newlength{\hxfoo}
\settodepth{\dyfoo}{\(\displaystyle\frac{\partial f}{\partial y}\)}
\settoheight{\hyfoo}{\(\displaystyle\frac{\partial f}{\partial y}\)}
\settodepth{\dxfoo}{\(\displaystyle\frac{\partial f}{\partial x}\)}
\settoheight{\hxfoo}{\(\displaystyle\frac{\partial f}{\partial x}\)}

\begin{document}
\[
\left(\frac{\partial f}{\partial x}\right)
\left(\frac{\partial f}{\partial \vphantom{y}x}\right)
\left(\frac{\partial f}{\partial y}\right)
\left(\raisebox{0pt}[\hyfoo][\dyfoo]{\(\displaystyle\frac{\partial f}{\partial x}\)}\right)
\left(\raisebox{0pt}[\hxfoo][\dxfoo]{\(\displaystyle\frac{\partial f}{\partial y}\)}\right)
\]
\end{document}

Compare the result:

Remark:

\left and \right delimiters are supposed to be symmetric around math axis. Hence the vertical difference in both delimiter are no larger than 2pt. So there shouldn't be any necessity to make the adjustment.