Suppose we have a function in Cartesian coordinates, z = f(x, y). Recall that Cartesian coordinates (x, y) can be related to Polar coordinates (r, θ) by x = r cos(θ) and y = r sin(θ).
a. Use the chain rule to find ∂z/ ∂τ and ∂z/ ∂θ in terms of ∂z/ ∂x and ∂z/ ∂y.
b. View the answers from (a) as two linear equations in two "unknowns" (∂z/ ∂x and ∂z/ ∂y). Solve these equations to write ∂z/ ∂x and ∂z/ ∂y terms of ∂z/ ∂τ and ∂z/ ∂θ.