# Notation Question for “Generalization of L’hopital’s Rule” PDF by V. V. Ivlev and I. A. Shilin

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?

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

## 1 Answer

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...

• 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. – Travis Asher Jan 2 at 15:13