Let $w(x,y,z)=\sqrt[\phantom{2}]{x^2+y^2+z^2}$ where $x=-2r{e}^t,y=7t{e}^r$ & $z=e^{rt}.$

Calculate $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{r}}$ & $\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{t}}by$ first finding $\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{r}},\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{r}},\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{r}},\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{t}},\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{t}}$ & $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{t}}$ and using the chain rule.

$\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{r}}=$

$\frac{\text{d}\text{e}\text{l}\text{w}}{\text{d}\text{e}\text{l}\text{t}}=$