Discussion Overview
The discussion revolves around the terminology used to describe derivatives that are not partial derivatives, specifically whether terms like "perfect derivative," "ordinary derivative," or "total derivative" are appropriate. The scope includes conceptual clarification and terminology in calculus.
Discussion Character
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant suggests that the partial derivative of a function g with respect to y is equivalent to what they term the "perfect derivative" of another function f, questioning the standard terminology.
- Another participant simply refers to it as the "derivative," indicating a lack of advanced calculus experience.
- A different participant argues that the partial derivative of g with respect to y should not be given a new name just because it coincides with the partial derivative of f with respect to x, emphasizing that it is simply a partial derivative.
- One participant states that in English, the term "ordinary" derivative is used to distinguish it from partial derivatives, similar to the distinction made in differential equations.
- Another participant agrees that "ordinary" derivative is a common term and adds that "total" derivative is also used, associating it with the concept of exact derivatives in functions of several variables.
- Another participant reiterates the term "total" derivative and connects it to the idea of exact derivatives, noting that for functions of one variable, the terms may be interchangeable.
Areas of Agreement / Disagreement
Participants express differing views on the appropriate terminology for derivatives that are not partial derivatives, with no consensus reached on a single term. Some propose "ordinary" or "total" derivatives, while others challenge the need for new terminology.
Contextual Notes
There are unresolved assumptions regarding the definitions and contexts in which these terms are applied, particularly concerning the distinction between ordinary and total derivatives in various mathematical settings.