- #1

kgal

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## Homework Statement

let z=f(x,y) be a differentiable function. If we change to polar coordinates, we make the substitution x=rcos(θ), y=rsin(θ), x^2+y^2=r^2 and tan(θ) = y/x.

a. Find expressions ∂z/∂r and ∂z/∂θ involving ∂z/∂x and ∂z/∂y.

b. Show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 + (1/r^2)(∂z/∂θ)^2.

## The Attempt at a Solution

a. i understand that f(x,y) in polar is f(r,θ) but don't understand how to calculate the partial derivatives of ∂z/∂x and ∂z/∂y because there is not know function for z...