I have a differential of a function, $df(x,y)=y\sin(xy)\mathrm{dx}+x\sin(xy)\mathrm{dy}$.
How do I determine the double partial derivatives $f_{xy}, f_{xx}$ and $f_{yy}$?
I am fairly certain I have to use the chain rule, but I can't see how to apply because of the $y$ and $x$ in the front.
If it's true that I should use the chain rule, could you give me a hint?