How $\frac{1}{2}\Delta(\epsilon \vec E^2)=\epsilon (\Delta \vec E) \cdot \vec E$
When I saw the expression, I thought they were differentiating (taking small changes in electric field)
$$\frac{1}{2}\Delta(\epsilon \vec E^2)=\frac{2}{2}\epsilon \vec E \Delta E$$ But I wonder where the dot product came from which confuses me about the expression.