Let u = f(x,y), where x = rcosθ and y = rsinθ. Using the chain
rules, carefully calculate the partial derivatives ∂u/ ∂r and ∂u/
∂θ , and the second partial derivatives ∂2u/ ∂r2 and ∂2u/ ∂θ2 , in
terms of r, θ, and the partial derivatives fx, fy, fxx, fxy,
fyy.
∂u /∂r =
∂u /∂θ =
∂^2u/ ∂r^2 =
∂^2u ∂θ^2=