Chain rule in Multivariable Calculus Question.

[AndreiRadulescu]

This is the question that has been given in an exam some years ago, and this is the solution part that I do not quite comprehend.


I cannot understand why you have partial derivative of g with respect to x and y, because if you use their hint and take u and v as they suggest, then you would have the partial derivatives with respect to u and v, not x and y.

 

[blamocur]

$\frac{\partial g}{\partial x}$ and $\frac{\partial g}{\partial u}$ mean the same thing here: a partial derivative of $g$ over its first variable. Same for $y$ and $v$.