Part 6 of 11 Find the following derivatives. Express your answer in terms of the independent variables. \( w_{s} \) and \( w_{t} \), where \( w=\frac{x-z}{3 y+z}, x=3 s+4 t, y=s t \), and \( z=3 s-4 t \) \( \frac{\partial w}{\partial y}=-\frac{3(x-z)}{(3 y+z)^{2}} \) \( \frac{\partial w}{\partial z}=-\frac{x+3 y}{(3 y+z)^{2}} \) (Type an expression using \( x, y \), and \( z \) as the variables.) \( \frac{\partial x}{\partial s}=3 \) (Type an expression using \( x, y \), and \( z \) as the variables.) \( \frac{\partial y}{\partial s}=t \) (Type an expression using \( s \) and \( t \) as the variables.) \( \frac{\partial z}{\partial s}=\square \) (Type an expression using \( s \) and \( t \) as the variables.) (Tyiables.)