Use the chain rule to find $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{s}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{t}},$ where

$z=e^{xy}tan(y),x=s5t,y=\frac{7s}{3t}$

First the pieces:

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}=$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}=$

$\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{s}}=$

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

$\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}\text{s}}=$

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

And putting it all together:

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{s}}=\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{x}}{\text{d}\text{e}\text{l}\text{x}}\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}}\frac{\text{d}\text{e}\text{l}\text{y}}{\text{d}\text{e}\text{l}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{z}=$del$\frac{z_{\text{d}\text{e}\text{l}\text{x}}}{?}$ delzdely