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I want to show the following equation with the maxwell equations: $$\frac{\partial}{\partial t}W+\vec{\nabla} \cdot \vec{S} = 0 $$

The problem is that I'm not understanding why I can do the following step:

$$\partial_t W=\partial_t \frac{1}{8\pi}(\vec{E}^2+\vec{B}^2)=\frac{1}{4\pi}(\vec{E}\partial_t\vec{E}+\vec{B}\partial_t\vec{B})$$

Can maybe someone explain it to me?

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    $\begingroup$ Which part of the equation are you struggling with? It looks like straight-forward differentiation to me... $\endgroup$
    – Philip
    Commented Mar 26, 2020 at 18:21

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\begin{align} \frac{\partial}{\partial t} \left( \vec{E} \cdot \vec{E} \right) =\; & \frac{\partial}{\partial t} \left( \sum_{i=1}^3 E_i^2 \right) \\ = & \sum_{i=1}^3 \frac{\partial}{\partial t} E_i^2 \\ = & \sum_{i=1}^3 2E_i \frac{\partial}{\partial t}E_i \\ = & \;2 \vec{E} \cdot \frac{\partial}{\partial t} \vec{E} \end{align}

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