Thread: Partial Derivative Proof (thermodynamics notation)

Show that:

I have Euler's chain rule and "the splitter." Also the property, called the "inverter" where you can reciprocate a partial derivative.

If I write Euler's chain rule, I only know how to write it when there are 3 variables, I usually write it in the form:


Where I can write x,y,z in any order as long as each variable is used in every spot. However, I do not know how to work this chain rule if I have an extra variable (u in this case).

I also tried using the "splitter" to do something like writing:


However, I do not know what to do with this because I have the term
, which doesn't appear in the original problem.

Any help would be appreciated.

Thanks in advance.

(This is for a thermodynamics course, but we are still in the mathematics introduction.)

i too am an engineer but i only took it to the undergrad lvl and am not familiar with this notation... can you clarify?

Sure thing.

If I say something like .

This means... The partial derivative of z with respect to x, holding y constant.

Originally Posted by Jacobpm64

Sure thing.

If I say something like .

This means... The partial derivative of z with respect to x, holding y constant.

There is no need to write,


Because the notation,

Means exactly that i.e. "you hold all variables constant except x".

Oh, i thought it was different in thermodynamics, Please excuse me.

^ im not sure i agree with your take on this, as this would simply cancel out the RHS of his eqn


i got the gerbils runnin, ill let u know if i come up with anything

There's a good argument here about this.

Scroll down to neutrino's post.

Partial derivative notation

I think that should clear things up about the notation.