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## Homework Statement

Show that ##\frac{\partial U}{\partial T}|_{N} = \frac{\partial U}{\partial T}|_{\mu} + \frac{\partial U}{\partial \mu}|_{T} \frac{\partial \mu}{\partial T}|_{N} ## (Pathria, 3rd Edition, pg. 197)

## Homework Equations

##U=TS + \mu N - pV##

## The Attempt at a Solution

I tried to take the derivative of U with respect with T at constant N and then at constant ##\mu## but I can't get the term on the right. I am not sure how can I get a product of 2 derivatives, because in taking derivatives in ##U=TS + \mu N - pV## I always have a derivative times a number (for example ##T\frac{\partial S}{\partial T}|_N##). What should I do? Is there another way other than using this formula?