What should we call the type of dervative that isn't a partial derivative?

[cmos]

For example, let f and g be defined as
$$f=x^2$$
$$g=2xy$$

I would say that the partial derivative of g with respect to y equals the perfect derivative of f(x). I've never been convinced that this is standard (or even correct) terminology. I am curious what some of you would use in place of perfect derivative.

 

[snipez90]

I thought it was just called the derivative :P. Then again I haven't taken anything beyond elementary calculus so I can't really say.

 

[Defennder]

Huh? The partial derivative of g wrt to y is just that. Just because the partial derivative of g wrt to y happens to be same as the partial derivative of f wrt x doesn't mean anything unless it's part of a certain class of DE problems. Why give it a new name?

 

[HallsofIvy]

In English, at least, that is called an "ordinary" derivative just as "ordinary" differential equations are distinguished form "partial" differential equations.

There is the concept of "exact" differentials in functions of several variables but that is a different matter. A differential f(x,y)dx+ g(x,y)dy is "exact" if and only if there exist a function, F(x,y), such that dF= f(x,y)dx+ g(x,y)dy.

 

[Dale]

In English, at least, that is called an "ordinary" derivative just as "ordinary" differential equations are distinguished form "partial" differential equations.

I have heard it called a "total" derivative also.

 

[HallsofIvy]

I have heard it called a "total" derivative also.

I would associate "total" derivative with "exact" derivative of a function of several variables. Of course, if we are talking about a function of one variable, they are all the same.