Find the following derivatives. \( z_{s} \) and \( z_{t} \), where \( z=e^{3 x+5 y}, x=8 s t \), and \( y=6 \mathrm{~s}+5 \mathrm{t} \) \( \frac{\partial z}{\partial x}=\square \) (Type an expression using \( x \) and \( y \) as the variables.)

To find \( z_s \) and \( z_t \) for the given function \( z = e^{3x + 5y} \) where \( x = 8st \) and \( y = 6s + 5t \), we start with the partial derivative of \( z \) with respect to \( x \). The derivative can be computed as follows: \[ \frac{\partial z}{\partial x} = \frac{\partial}{\partial x} \left(e^{3x + 5y}\right) = 3e^{3x + 5y} \] Now you have \( \frac{\partial z}{\partial x} = 3e^{3x + 5y} \).