Understanding the Exact Differential Notation in Multivariable Calculus

[GoldPheonix]

I'm studying calculus III topics on my own, but I've seen this notation prop up a lot. Could you tell me what it means?

http://en.wikipedia.org/wiki/Exact_differential

The notation on this page, it has this notation:

$$( \frac{dA}{dx} )_y = ( \frac{dB}{dy} )_x$$

What do the x's and y's mean as subscript of the parenthesis? Just plug in the y value at that point into that derivative's equation?

 

[gabee]

That's a common way of denoting a partial derivative--in other words, if F is a function, then F_x is the partial derivative of F with respect to x.

 

[GoldPheonix]

But it's already taking the partial derivative with respect to x, and in the other, y. What's up with that?

 

[gabee]

OH, sorry, actually in that case I think the notation $$\left( \frac{\partial A}{\partial y} \right)_{x}$$ means "the partial derivative of A with respect to y, holding x constant." See the last example under "Notation" here: http://en.wikipedia.org/wiki/Partial_differential#Notation

 

[GoldPheonix]

Thank you.