How to take derivative with respect to a variable of a function of two variables and another function

Question

I have a function $f(x-a,y-b\frac{1}{g(x,y)})$. I want to find the partial derivative of this function with respect to $x$. But I am literally lost. Can you give me any insight on the solution?What I could do so far is as follows: $$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial g}\frac{\partial g}{\partial x}$$ I am stuck at the point in calculation of $\frac{\partial f}{\partial g}$. Thanks in advance. Have a nice day!