Translations:Dictionary:Calculus of variations/32/en

${\frac {d}{dt}}\left[{\frac {\partial L}{\partial {\dot {x}}}}\right]={\frac {\partial ^{2}L}{\partial t\partial x}}+{\frac {\partial ^{2}L}{\partial x\partial {\dot {x}}}}{\frac {dx}{dt}}+{\frac {\partial ^{2}L}{\partial {\dot {x}}^{2}}}{\frac {d^{2}x}{dt^{2}}}={\frac {\partial ^{2}L}{\partial x\partial {\dot {x}}}}{\frac {dx}{dt}}+{\frac {\partial ^{2}L}{\partial {\dot {x}}^{2}}}{\frac {d^{2}x}{dt^{2}}}$