If $\overrightarrow η \;$ is a unit normal outward vector on $\partial B(y,\varepsilon )\;$ where $B(y,\varepsilon )\;$ is a sphere on $\mathbb R^3\;$, why does this: $\frac {\partial}{\partial \overrightarrow η}=-\frac {\partial}{\partial r}\;$ hold?
NOTE: $r=\vert x-y \vert\;\;\forall x,y \in \mathbb R^3$
I'm really struggling with this. Directional derivatives confuse me a lot! I would appreciate if someone could make that clear to me..
Thanks in advnace!!