You're right on part a. Why don't you try this for part (b)?
This will be very useful when you think about vector fields that go like such as electric fields.
Sorry for the naff title, couldn't think of anything else. I've ended with a ridiculous answer...
a) Find , where , and is a differentiable function.
b) In Part (a), find such that .
I ended up with something like for part a), which I highly doubt is right thus I can't really attempt part b)... cheers in advance.