Nomenclature

[JeffM]

\(\displaystyle y = f(x_1, ...\ x_n),\ where\ n > 1,\ and \dfrac{\delta y }{\delta x_i} = g_i(x_i)\ for\ 1 \le i \le n.\)

Is there a standard name for such a function or its variables?

 

[daon2]

It is a real-valued function on n variables (\(\displaystyle \mathbb{R}^n\) to \(\displaystyle \mathbb{R}\)). But I doubt that's what you're asking for. If your \(\displaystyle g_i(x_i)\) are continuous then \(\displaystyle f\) is a also a differentiable function.

 

[JeffM]

It is a real-valued function on n variables (\(\displaystyle \mathbb{R}^n\) to \(\displaystyle \mathbb{R}\)). But I doubt that's what you're asking for. If your \(\displaystyle g_i(x_i)\) are continuous then \(\displaystyle f\) is a also a differentiable function.

No. What I was asking about is a differentiable real function with multiple independent variables, but the partial derivative with respect to each independent variable is a function of only that variable.

Sorry should have been more specific. It is the reduction of the partials to functions of one variable that I am asking about.

 

[JeffM]

Wait. Maybe there is no such function. That would certainly explain why I do not know a name for it.

 

[daon2]

I don't know of a special name, no, but there are some of course. A simple case being a polynomial with no "combined" terms.

e.g.

\(\displaystyle f(x,y,z) = x^2+y^2+z^2\).

 

[JeffM]

Thank you.