If z = f(x, y) and x = r cos(θ), y = r sin(θ), find ∂z/∂r.
Correct: A
By the chain rule, ∂z/∂r = (∂z/∂x)(∂x/∂r) + (∂z/∂y)(∂y/∂r). Since x = r cos(θ), ∂x/∂r = cos(θ). Since y = r sin(θ), ∂y/∂r = sin(θ). Therefore, ∂z/∂r = (∂z/∂x)cos(θ) + (∂z/∂y)sin(θ).