9. Let

f, 9 : R2 ---t R be differentiable and satisfy the Cauchy-Riemann equations, i.e., that af = ag and af = _ ag ax ay ay ax .

If u(r, B) = f(r cos B, r sin B), and v(r, B) = g(r cos B, r sin B), prove that au 1 av

=

ar -:;: aB'

av 1 au ar r aB r # o.