I am struggling with this problem from Widder's "Advanced Calculus" (Chapter 1 section 1 problem 2 of the first edition).
If $f(x,y,z) = x\log(y^2) +ye^z$, find $f_2(x,xy,y-z)$.
Specifically, I don't understand what the notation $f_2(x,xy,y+z)$ means. Am I supposed to differentiate with respect to $y$ and then substitute $y=xy$ and $z=y+z$?
Note: it seems that Widder uses "log" meaning "ln". Does anyone know why?
My interpretation would be ; $$f(r,s,t)=2r\ln s+se^t,$$$$ g(x,y,z)=f(x,xy,y-z)$$$$\text{ Find }\frac{\partial g}{\partial y}.$$