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MathTEST

$\sin ^{2}(x)+\cos(x)^{2}+e^{i\pi }+0$

Mediawiki-Math: $\sin(x)^{2}+\cos(x)^{2}+e^{i\pi }=0$

${\begin{aligned}&{\frac {d}{dt}}{\frac {\partial L({\bar {r}},{\bar {v}},t)}{\partial {{v}_{k}}}}=m{{\ddot {x}}_{k}}+q\left({\frac {\partial }{\partial t}}{{A}_{k}}({\bar {r}},t)+{\frac {\partial {{A}_{k}}({\bar {r}},t)}{\partial {{x}_{l}}}}{\frac {\partial {{x}_{l}}}{\partial t}}\right)=m{{\ddot {x}}_{k}}+q\left({\frac {\partial }{\partial t}}+{\bar {v}}\cdot \nabla \right){{A}_{k}}({\bar {r}},t)\\&{\frac {\partial L({\bar {r}},{\bar {v}},t)}{\partial {{x}_{k}}}}=q\left[{\frac {\partial }{\partial {{x}_{k}}}}\left({\bar {v}}{\bar {A}}\right)-{\frac {\partial }{\partial {{x}_{k}}}}\Phi \right]\\&\Rightarrow 0={\frac {d}{dt}}{\frac {\partial L({\bar {r}},{\bar {v}},t)}{\partial {{v}_{k}}}}-{\frac {\partial L({\bar {r}},{\bar {v}},t)}{\partial {{x}_{k}}}}=m{{\ddot {x}}_{k}}+q\left({\frac {\partial }{\partial t}}+{\bar {v}}\cdot \nabla \right){{A}_{k}}({\bar {r}},t)-q\left[{\frac {\partial }{\partial {{x}_{k}}}}\left({\bar {v}}{\bar {A}}\right)-{\frac {\partial }{\partial {{x}_{k}}}}\Phi \right]\\&=m{{\ddot {x}}_{k}}+q{\frac {\partial }{\partial t}}{{A}_{k}}({\bar {r}},t)+q\left[\left({\bar {v}}\cdot \nabla \right){{A}_{k}}({\bar {r}},t)-{\frac {\partial }{\partial {{x}_{k}}}}\left({\bar {v}}{\bar {A}}\right)\right]+q{\frac {\partial }{\partial {{x}_{k}}}}\Phi \\&\left[\left({\bar {v}}\cdot \nabla \right){{A}_{k}}({\bar {r}},t)-{\frac {\partial }{\partial {{x}_{k}}}}\left({\bar {v}}{\bar {A}}\right)\right]=-{{\left[{\bar {v}}\times \left(\nabla \times {\bar {A}}\right)\right]}_{k}}\\&\Rightarrow 0=m{\ddot {\bar {r}}}+q{\frac {\partial }{\partial t}}A({\bar {r}},t)-q\left[{\bar {v}}\times \left(\nabla \times {\bar {A}}\right)\right]+q\nabla \Phi =m{\ddot {\bar {r}}}+q\left[{\frac {\partial }{\partial t}}A({\bar {r}},t)+\nabla \Phi -\left[{\bar {v}}\times \left(\nabla \times {\bar {A}}\right)\right]\right]\end{aligned}}$

${\underline {b}}$

${\begin{aligned}a&+b\\\\c&+d\end{aligned}}$

${\text{Magnetfeld}}\quad$

${\underline {\nabla }}$ $c+c*c^{2}+c+2c+8+\cos ^{2}x+y$

${\begin{aligned}{\text{Magnetfeld}}\quad {\underline {B}}&={\underline {\nabla }}\times {\underline {A}}\\{\text{elektrisches Feld}}\quad {\underline {E}}&=-{\underline {\nabla }}\phi -{\frac {1}{c}}{{\partial }_{t}}{\underline {A}}\\{\text{one or about spaces}}\end{aligned}}$