Clarification on Partial Derivative Symbols

[erok81]

Homework Statement

See uploaded image.

Homework Equations

n/a

The Attempt at a Solution

I’ve never seen this format so I am not sure what it is asking. Taking L1.B as an example. They are partials, but does it mean partial of x with respect to z? And then partial of y with respect to z? I am pretty sure that part is right after looking at it again.

The one I am really confused about it L1.3D. There are two partial symbols with y and z in front of w. Maybe partial of x then y with respect to w?

And I guess the same thing with C. Partial of c1? Since c is a constant wouldn’t that be zero every time? There is no x with the partial symbols, so I don't think I do anything with the x or y?

I have only seen the following when referring to partial derivatives...

$$\frac{\partial x}{\partial y}$$
(partial of x with respect to y)

And...

$$F_{x}$$
(partial of x)

 

[lanedance]

read it as follows:
$$\partial_x = \frac{\partial }{\partial x}$$

 

[Raskolnikov]

When in doubt, search Google/Wiki ;)! http://en.wikipedia.org/wiki/Partial_derivative

3B. partial of z with respect to x...and partial of z with respect to y.
3C. I'm not sure on this one. I guess partial of u w/ respect to c1, c2, c3, separately.
3D. partial of w with respect to y and then partial with respect to x.

 

[erok81]

Perfect, that is what I was thinking. Thanks for the responses.

Back to the c1, c2, c3... since those are constants, isn't that just going to be zero? Or am I missing something still?

 

[Dick]

Perfect, that is what I was thinking. Thanks for the responses.

Back to the c1, c2, c3... since those are constants, isn't that just going to be zero? Or am I missing something still?

Why do you think c1, c2 and c3 are constants? If you are taking partial derivatives of them, you shouldn't be thinking of them as constants.

 

[Raskolnikov]

Just assume x is not a function of c1, c2, or c3, and go from there.

 

[erok81]

Got it. I guess I am used to c being used as a constant. Plus we just did separation of variables where c1 and c2 where used as constants. With that and the fact that they were before the variables, like most constants, I just assumed that's why they were.

No matter how much I do these, I always get thrown off when different variables get used. :rofl: