Let $u=u(x,y),v=v(x,y)$ satisfy the Cauchy$-$Riemann equations:

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}=\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}},\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}=-\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{x}}.$

Find a pair $of$ equations satisfied $by\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{r}},\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}},\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{r}},$ and $\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}}.$