I'm just in need of some clearing up of how to differentiate the lagrangian with respect to the covariant derivatives when solving the E-L equation:(adsbygoogle = window.adsbygoogle || []).push({});

Say we have a lagrangian density field

\begin{equation}

\mathcal{L}=\frac{1}{2}(\partial_{\mu}\hat{\phi})(\partial^{\mu}\hat{\phi})

\end{equation}

When solving for E-L why does:

\begin{equation}

\frac{\partial \mathcal{L}}{\partial (\partial_{\mu}\phi)}= \partial^{\mu}\hat{\phi}

\end{equation}

i.e Why do we lose the factor of 1/2

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# I Lagrangian differentiation

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