(You ought to if you're studying multivariable calculus. If you don't, then the question you have posted is not your immediate problem. Your immediate problem would be to urgently review all of the pre-requisite single variable calculus that your instructor will assume you already know).
Then you know how to calculate the partial derivatives and .
Your linear approximation formula is the wrong one to use for this question. You have quoted the single variable formula. The formula required is the two variable formula. It will be in your classnotes or textbook. I suggest you find it (and then review all the examples that will follow it).