Use the chain rule to find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$, where $$z = e^{xy}\tan y, x = 5 s + 5 t, y = \frac{7 s}{2 t}$$
First the pieces:
$\frac{\partial z}{\partial x} =$ $\frac{\partial z}{\partial y} =$
$\frac{\partial x}{\partial s} =$ $\frac{\partial x}{\partial t} =$
$\frac{\partial y}{\partial s} =$ $\frac{\partial y}{\partial t} =$
And putting it all together:
$\frac{\partial z}{\partial s} = \frac{\partial z}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial z}{\partial y}\frac{\partial y}{\partial s}$ and $\frac{\partial z}{\partial t} = \frac{\partial z}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial z}{\partial y}\frac{\partial y}{\partial t}$