Double partial derivative with chain rule

This video seeks to explain how to take the second partial derivative of a function f(x,y) where x = rcosθ and y = rsinθ. Unfortunately, my memory card filled up before I finished the problem. After some reflection, I believe it makes more sense to write the final answer in terms of x and y rather than r and θ. With that said, the final answer should be: f_(xx) * y^2 - 2 f_(xy) * xy + f_(yy) x^2 - f_(x) * x - f_(y) * y