Lets say we have a function: .

We want to find all point that is it differentiable. Right of the bat we know that it is differentiable for . For is a "direct" function of . E.g. we do not have to appeal to CR equations.

Also it is not differentiable for since is not a "direct" function of .

Now for can we use the same argument to show that is not differentiable there?

Because then we have . And this is not a "direct" function of .