Use the chain rule here..

For , we know by the chain rule that

We can figure out that .

To find , use partial implicit differentiation:

We also can figure out that . We can disregard the term, since it will end up disappearing.

Thus, we now see that

Since, , we see that

Now evaluate it at (0,0). You should end up with

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Try to find using the same technique as I used above.

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For finding , recall that by the chain rule, we have (I think I have this correct...if not, feel free to state what it should be)

Follow the same process for this one as well.

Does this make sense?

--Chris