Just as the headline says, what is the difference between $(\frac{\partial F}{\partial T})_X$ and $\frac{\partial F}{\partial T}$ ? The former is used at least in thermodynamics, and I find the notation a bit confusing. In taking partial derivatives we are already considering all arguments but $T$ to be constant - what new information do we get by specifying $X$ as a constant?
To me it seems like $(\frac{\partial F}{\partial T})_X$ is equal to taking a total derivative first, and then assigning $X$ to be constant, and simplifying the total derivative from there. Am I correct?
If you want to show by example, please use something complicated enough, such as $F(T,X,Y)$ so that $X$ and $Y$ might depend on $T$.
Thank you in advance =).