Let variable $x \in \mathbb{R}^n$ and let $\theta \in \mathbb{R}^n$ be a constant. We have 2 other variables $s \in \mathbb{R}$ and $y \in \mathbb{R}^n$ such that $x = s\theta + y$. In my course notes, they state: $dx = dsdy$ But how we get to this equation? My first idea was $dx = d(s \theta + y) = d(s \theta) + d(y) = d(s) \theta + d(y)$ but this doesn't give me what I need. Can someone help me?
EDIT: Maybe this is something you need, but y is a variabele that is always perpendicular to $\theta$ . This implies that $\theta .x = s$
EDIT: I misunderstood the statement in my course notes, my excuses. You can totally ignore this question