Turn differential upside down?

Asked Nov 08 '17 at 21:27

Active Nov 08 '17 at 21:27

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I saw some theoretical physics exercise and found a statement like $\frac{\partial V}{\partial p}=f$. In the next step the author concluded $\frac{\partial p}{\partial V}=\frac{1}f$.

This conclusion looks terribly wrong to me, but seems to work in the given example.

Now I wonder: Are there any mathematical conditions that would allow such a conclusion?

asked Nov 08 '17 at 21:27

meneken17

2

We need to be able to write $p(V)$, of course, which requires that $V$ be invertible at the point $p$ in question, i.e. $p(V(p)) = p$ (forgive my abuse of notation). Then, it follows neatly from the derivative rule for inverse functions. – Michael L. Nov 08 '17 at 21:30
1

Possible duplicate of "Reciprocal" of derivatives – ultrainstinct Nov 08 '17 at 22:06

Turn differential upside down?

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