Q: The derivative of the normal direction passing by a point according to a translation of the point Suppose given a point $P(x_p,y_p)$ and a curve described by an implicit equation $f(x,y,z)=0$
How to calculate the derivative of the normal direction passing by $P$ according to a translation of the point $P$ in $x$ direction?
I mean if the the point $P$ is translated in $x$ direction by $\delta x$ to obtain a point $P'$, what will be the difference between the new and the old normal direction.
Could we assume that the derivative of the normal according to the translation is the same as the derivative according to $x$?
