Find the derivative \( \frac{d w}{d t} \), where \( w=6 x y z, x=4 t^{4}, y=t^{-1} \), and \( z=2 t^{-3} \). \( \frac{\partial w}{\partial x}=\square \) (Type an expression using \( x, y \), and \( z \) as the variables.)

To find the partial derivative \( \frac{\partial w}{\partial x} \) where \( w = 6xyz \), we first differentiate with respect to \( x \). Using the product rule, we treat \( y \) and \( z \) as constants while differentiating with respect to \( x \): \[ \frac{\partial w}{\partial x} = 6 \cdot y \cdot z \] Thus, the expression using \( x, y, \) and \( z \) is: \[ \frac{\partial w}{\partial x} = 6yz \]