Stretch cases in order to be "more inclusive"

Question

Regarding the dcases environment, I noticed that, even if now I have all the math symbols extended (for example frac), when using derivatives the bracket doesn't actually cover completely the space needed from the math symbols.

Let's take the following example

given by the code

\[
    \begin{dcases}
        \frac{\partial U}{\partial l}\mathrm{d} l = 
        (\mathrm{d} U)_{\theta=\text{cost}} = \nabla U \cdot\mathrm{d}\boldsymbol{l} = 
        -\nabla(\boldsymbol{E}_0 \cdot\boldsymbol{p})\cdot\mathrm{d}\boldsymbol{l}\\
        \\
        \frac{\partial U}{\partial \theta}\mathrm{d}\theta = 
        \frac{\partial}{\partial\theta}(-E_0p\cos\theta)\mathrm{d}\theta = 
        E_0p\sin\theta\mathrm{d}\theta =
        \boldsymbol{E}_0\times\boldsymbol{p}\cdot\mathrm{d}\boldsymbol{\theta}
    \end{dcases}
\]

As you can notice - if you don't, look at the next image - the derivatives escape the brace, even if for a microscopic portion.

Now, I understand it sounds like I'm a maniac, but this thing break the harmony of my LaTeX, so I'm desperately looking for a solution. I thought that it would be very nice if there were some options to the dcases environment to stretch a little bit more the cases, but if there're not such "facilities" how could it be solved?

Answer 1

I agree with egreg that it is nothing to worry about, but one could (and I did below) add a "strut" to the \partial U in the top equation and to the \partial \theta in the bottom equation. As barbara notes, if the strut is a mere \strut, it may introduce a little unwanted vertical spacing, and so I define \htstrut to mask the depth and use it or \strut accordingly.

\documentclass{article}
\usepackage{mathtools,tabstackengine}
\newcommand\htstrut{\setbox0=\hbox{\strut}\dp0=0pt}
\begin{document}
\[
    \begin{dcases}
        \frac{\partial U\htstrut}{\partial l}\mathrm{d} l = 
        (\mathrm{d} U)_{\theta=\text{cost}} = \nabla U \cdot\mathrm{d}\boldsymbol{l} = 
        -\nabla(\boldsymbol{E}_0 \cdot\boldsymbol{p})\cdot\mathrm{d}\boldsymbol{l}\\
        \\
        \frac{\partial U}{\partial \theta\strut}\mathrm{d}\theta = 
        \frac{\partial}{\partial\theta}(-E_0p\cos\theta)\mathrm{d}\theta = 
        E_0p\sin\theta\mathrm{d}\theta =
        \boldsymbol{E}_0\times\boldsymbol{p}\cdot\mathrm{d}\boldsymbol{\theta}
    \end{dcases}
\]
\end{document}

Alternately, one could change the dcases to an aligned, place the data in the 2nd field of the aligned, then \addstackgap[<length>] to the aligned, and apply a \left\{. In this case, no \strut is required.

\documentclass{article}
\usepackage{mathtools,stackengine}
\stackMath
\begin{document}
\[
    \left\{\addstackgap[4pt]{\begin{aligned}
        &\frac{\partial U}{\partial l}\mathrm{d} l = 
        (\mathrm{d} U)_{\theta=\text{cost}} = \nabla U \cdot\mathrm{d}\boldsymbol{l} = 
        -\nabla(\boldsymbol{E}_0 \cdot\boldsymbol{p})\cdot\mathrm{d}\boldsymbol{l}\\
        \\
        &\frac{\partial U}{\partial \theta}\mathrm{d}\theta = 
        \frac{\partial}{\partial\theta}(-E_0p\cos\theta)\mathrm{d}\theta = 
        E_0p\sin\theta\mathrm{d}\theta =
        \boldsymbol{E}_0\times\boldsymbol{p}\cdot\mathrm{d}\boldsymbol{\theta}
    \end{aligned}}\right.
\]
\end{document}

Above, I added a 4pt gap above and below the aligned environment. If I had chosen 8pt, for example, it would have looked like this:

Answer 2

You simply can use the empheq environment to do that. Needless to load amsmath since the former loads mathtools, which loads amsmath.

I also improved the spacing of you differentail symbol, defining a \dd command; and simplified the typing of partial differentials with the esdiff package.

\documentclass{article}
\usepackage{empheq, esdiff}

\newcommand*{\dd}{\mathop{\kern0pt\mathrm{d}}\mkern-2mu{}}


\begin{document}

\begin{empheq}[left=\empheqlbrace]{align*}
     & \diffp{U}{l}\dd l =
    (\dd U)_{\theta=\text{cost}} = \nabla U \cdot\dd \boldsymbol{l} =
    -\nabla(\boldsymbol{E}_0 \cdot\boldsymbol{p})\cdot\dd\boldsymbol{l}\\
    \\
    & \diffp{U}{\theta}\dd\theta =
    \diffp{}{\theta}(-E_0p\cos\theta)\dd\theta =
    E_0p\sin\theta\dd\theta =
    \boldsymbol{E}_0\times\boldsymbol{p}\cdot\dd\boldsymbol{\theta}
\end{empheq}

\end{document}