While not quite accessible to anyone interested in mathematics, this problem is a good challenge for anyone who has finished their calculus courses and needs a refresher. As usual, I've posted my solution below...
Taking the derivatives of this function required a chain rule within the quotient rule. As long as you're neat with your variables, it shouldn't be too difficult to work out. At the end we have a gradient vector that looks messier than our original problem!
See you all next week for another challenge problem.