Within this brief text starting on page 2, the author(s) have a habit of employing a sort of "mixed" notation of differentiation, mixing the "prime marks" of Lagrange's notation for differentiation of a single-variable with the subscript notation commonly used in partial differentiation; that is, something like:

f 'x (x0,y0)

Now, being that this text has had a few errors that I have noticed already, this could simply be an accidental use of the Lagrange notation via force of habit for performing differentiation; however, being that this "error" is repeated throughout the document, I find this unlikely to be the case. Might it be that this is some sort of abuse of notation used to represent a more common mathematical concept? If so, what mathematical concept might that be?

  • $\begingroup$ $f'_x(x_0,y_0)$ is a Russian/exUSSR notation for the partial derivative and means just the same as $f_x(x_0,y_0)$. $\endgroup$ – AVK Jan 2 at 16:38

I guess that if you view $f'(x_0, y_0)$ as a row vector and denote its components with $x$ or $y$ subscripts (in physics this is often done for vectors) then $f'_x(x_0, y_0)$ would actually be the partial derivative w.r.t $x$ of $f$ at $(x_0, y_0)$.

I haven't seen that notation ever before however. Maybe it's a Russian thing...

  • $\begingroup$ You know, that seems to make sense, as this notation is first used to make use of the requirement that [ f'_x (x_0,y_0) ]^2 + [ f '_y (x_0,y_0) ]^2 be nonzero; this would be synonymous to requiring the magnitude of the gradient of f to be nonzero using your notation assumption, which certainly seems reasonable. I appreciate this response, thanks! *Edited because mini-markdown does not support the "<>" formatting notations. $\endgroup$ – Travis Asher Jan 2 at 15:13

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