Difference Between \partial x and d x in Derivatives?

[KStolen]

Hi, this may seem like a silly question but here goes :
Is there any difference between writing $$\partial x$$ and $$d x$$ when referring to partial derivatives? I've always used the simple $$d x$$ for both because I don't like drawing the curvy d. To me, $$\partial N / d x$$ and $$d N / d x$$ are the same really.

However, if in an exam I was asked to state a theorem (say Green's theorem), should I use the partial derivative symbol when writing the equation?
How about when I actually use the theorem?]

 

[Mark44]

Hi, this may seem like a silly question but here goes :
Is there any difference between writing $$\partial x$$ and $$d x$$ when referring to partial derivatives? I've always used the simple $$d x$$ for both because I don't like drawing the curvy d. To me, $$\partial N / d x$$ and $$d N / d x$$ are the same really.

They aren't the same, so you shouldn't use the straight derivative when a partial derivative is called for. Also, don't mix the notation. The partial of f with respect to x is written as
$$\frac{\partial f}{\partial x}$$
not as
$$\frac{\partial f}{dx}$$

Here f would be a function of two or more variables, such as f(x, y) = 2x + 3y². Assuming that x and y are independent, it wouldn't make any sense to talk about df/dx.

For this simple example,
$$\frac{\partial f}{\partial x} = 2$$
and
$$\frac{\partial f}{\partial y} = 6y$$

If you don't like this style of notation, there's another that is used, with subscripts. f_x represents the partial of f with respect to x. In the example I gave, f_x = 2 and f_y = 6y.

However, if in an exam I was asked to state a theorem (say Green's theorem), should I use the partial derivative symbol when writing the equation?
How about when I actually use the theorem?]