Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$?
1. $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1} \\$
2. $\dfrac{x \: \text{ln } \phi}{\text{ln } \phi \text{ ln } \psi -1} \\$
3. $\dfrac{\text{ln } \phi}{\text{ln } \phi \text{ ln } \psi -1} \\$
4. $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1}$