1
$\begingroup$

What is wrong with the following naive derivation of the triple product rule ( https://en.wikipedia.org/wiki/Triple_product_rule)

$\frac{\partial X}{\partial Y}=\frac{\partial X}{\partial Z}\frac{\partial Z}{\partial Y}\Rightarrow\\ \left(\frac{\partial X}{\partial Z}\right)^{-1}\left(\frac{\partial Z}{\partial Y}\right)^{-1}\frac{\partial X}{\partial Y}= \frac{\partial Z}{\partial X}\frac{\partial Y}{\partial Z}\frac{\partial X}{\partial Y}=1\ne-1$

$\endgroup$
  • $\begingroup$ Your first line is wrong, you have used the chain rule for a function who's variables are not functions of another variable. $\endgroup$ – jake walsh Dec 9 '17 at 22:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.