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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. $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1}$
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