In my electromagnetism book there is an equality I am not getting:
$\vec{H} \cdot \frac{\partial \vec{H}}{\partial t} = \frac{1}{2} \frac{\partial(\vec{H} \cdot \vec{H})}{\partial t}$.
Where does the factor $\frac{1}{2} come from?$
Any help is appreciated!
This follows from the product rule for the dot product: $$ \frac{\partial}{\partial t}(\vec{H}\cdot\vec{H})= \frac{\partial\vec{H}}{\partial t}\cdot\vec{H} + \vec{H}\cdot\frac{\partial\vec{H}}{\partial t} = 2\vec{H}\cdot\frac{\partial\vec{H}}{\partial t}$$