I have two vectors $\vec{A}$ and $\vec{B}$ as shown below:
The point at the origin of vector $\vec{B}$ has coordinates $(x,y)$. The angle between the two vectors is $\theta$.
Now in my physics book there is an expression $\dfrac{\partial(\cos\theta)}{\partial x}$. How does this expression makes sense?
At point $(x,y)$, there is a vector $\vec{B}$. But at point $(x+dx,y)$, there should be no vector.
By changing $dx$ (i.e. by moving the point from $(x,y)$ to $(x+dx,y)$) we only change the point, not the whole vector. If someone says that the whole vector needs to be moved, how can we prove it mathematically?
Edit: Simplified version of a part of the treatise
