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Little differentiation question

In my notes, it says this:


But I don't understand how it differentiates to that. Shouldn't it be this?


I know that the notes' result is correct, but I don't understand how it was derived!
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Original post by Plagioclase
In my notes, it says this:


But I don't understand how it differentiates to that. Shouldn't it be this?


I know that the notes' result is correct, but I don't understand how it was derived!


this is partial
you treating it as a chain rule of a full differential

if you diff wrt z partially strictly speaking the derivatives should be the other way but since they commute they wrote it like this
Original post by Plagioclase
In my notes, it says this:


But I don't understand how it differentiates to that. Shouldn't it be this?


I know that the notes' result is correct, but I don't understand how it was derived!

The first result makes sense yes (ug is a function of P so think of everything else as a constant). How did you get the second result?

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