Points: 0 of 1 Sav list 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 \( z=3 s-4 t \) (lype an expression using \( s \) and \( t \) as the vanables.) \[ \frac{\partial y}{\partial s}=\bar{t} \] (Type an expression using \( s \) and \( t \) as the variables.) \[ \frac{\partial z}{\partial s}=3 \] (Type an expression using \( s \) and \( t \) as the variables.) \[ \frac{\partial x}{\partial t}=4 \] (Type an expression using \( s \) and \( t \) as the variables.) \[ \frac{\partial y}{\partial t}=\bar{s} \] 12 (Type an expression using \( s \) and \( t \) as the variables.) \[ \frac{\partial z}{\partial t}=\square \] 13 (Type an expression using s and \( t \) as the variables.)

To find the derivatives requested, we analyze each expression based on the definitions of \(x\), \(y\), and \(z\): 1. Given \( z = 3s - 4t \), we differentiate with respect to \( t \): \[ \frac{\partial z}{\partial t} = -4 \] 2. The partial derivatives based on the provided expressions would be: \[ \frac{\partial y}{\partial s} = t \quad (\text{from \(y = st\)}) \] \[ \frac{\partial y}{\partial t} = s \quad (\text{from \(y = st\)}) \] \[ \frac{\partial x}{\partial s} = 3 \quad (\text{from \(x = 3s + 4t\)}) \] 3. Lastly, for the expression \(\frac{\partial x}{\partial t}\): \(\frac{\partial x}{\partial t} = 4\) is already given. So, your results in terms of \(s\) and \(t\) are: 1. \[ \frac{\partial z}{\partial t} = -4 \] 2. \[ \frac{\partial y}{\partial s} = t, \quad \frac{\partial y}{\partial t} = s, \quad \frac{\partial z}{\partial s} = 3, \quad \frac{\partial x}{\partial s} = 3, \quad \frac{\partial x}{\partial t} = 4 \]