If we have : $f=f(x,y)$,
then what does the following mean and how to compute it : $(dy/dx)_f$ ?
Note : This was found in a mathematics textbook destined for physicists. If it is used differently by mathematicians, I'm interested in its use in physics.
Thank you.
It means the derivative is evaluated at fixed $f$, thereby regarding $y$ as a function of $x$. This is more commonly seen with partial derivatives. For other notation, see here viz. @ncmathsadist.