Chapter 15.10, Problem 6P

By expanding $w(x,y,z)$ in a three-variable power series similar to $(10.10),$ show that $r_w=\sqrt{{\left(\frac{\partial w}{\partial x}\right)}^2{r}_x^2+{\left(\frac{\partial w}{\partial y}\right)}^2{r}_y^2+{\left(\frac{\partial w}{\partial z}\right)}^2{r}_z^2}$