I think all they want is that, since , and are all differentiable, then their product and sum is differentiable.
This is not true in regards to division, like .
Determine whether or not is differentiable.
Now, from what I understand, in order to show that a function of two variables is differentiable at some point , I have to show that and are continuous at and that itself is continuous at . I know that the partials are continuous for all , but how do I show that is continuous? (The problem does not ask if the function is differentiable at a specific point .) Thanks in advance.
Same question with the equation .