Editing Euler–Lagrange equation (section)

===Single function of two variables with higher derivatives===
If there is a single unknown function ''f'' to be determined that is dependent on two variables ''x''<sub>1</sub> and ''x''<sub>2</sub> and if the functional depends on higher derivatives of ''f'' up to ''n''-th order such that
: <math>
   \begin{align}
     I[f] & = \int_{\Omega} \mathcal{L}(x_1, x_2, f, f_{1}, f_{2}, f_{11}, f_{12}, f_{22},
                                        \dots, f_{22\dots 2})\, \mathrm{d}\mathbf{x} \\
     & \qquad \quad
        f_{i} := \cfrac{\partial f}{\partial x_i} \; , \quad
        f_{ij} := \cfrac{\partial^2 f}{\partial x_i\partial x_j} \; , \;\; \dots
   \end{align} 
</math>
then the Euler–Lagrange equation is<ref name=Courant/>
:<math>
  \begin{align}
    \frac{\partial \mathcal{L}}{\partial f}
    & - \frac{\partial}{\partial x_1}\left(\frac{\partial \mathcal{L}}{\partial f_{1}}\right)
      - \frac{\partial}{\partial x_2}\left(\frac{\partial \mathcal{L}}{\partial f_{2}}\right) 
      + \frac{\partial^2}{\partial x_1^2}\left(\frac{\partial \mathcal{L}}{\partial f_{11}}\right)
      + \frac{\partial^2}{\partial x_1\partial x_2}\left(\frac{\partial \mathcal{L}}{\partial f_{12}}\right)
      + \frac{\partial^2}{\partial x_2^2}\left(\frac{\partial \mathcal{L}}{\partial f_{22}}\right) \\
    & - \dots
      + (-1)^n \frac{\partial^n}{\partial x_2^n}\left(\frac{\partial \mathcal{L}}{\partial f_{22\dots 2}}\right) = 0
  \end{align}
 </math>
which can be represented shortly as:
:<math>
    \frac{\partial \mathcal{L}}{\partial f} +\sum_{j=1}^n \sum_{\mu_1 \leq \ldots \leq \mu_j} (-1)^j \frac{\partial^j}{\partial x_{\mu_{1}}\dots \partial x_{\mu_{j}}} \left( \frac{\partial \mathcal{L} }{\partial f_{\mu_1\dots\mu_j}}\right)=0
 </math>
wherein <math>\mu_1 \dots \mu_j</math> are indices that span the number of variables, that is, here they go from 1 to 2. Here summation over the <math>\mu_1 \dots \mu_j</math> indices is only over <math>\mu_1 \leq \mu_2 \leq \ldots \leq \mu_j</math> in order to avoid counting the same [[partial derivative]] multiple times, for example <math>f_{12} = f_{21}</math> appears only once in the previous equation.