Is the Relationship Between Natural Log and Partial Derivatives in PDE Valid?

[Hypatio]

Is the following relationship true?:

$\frac{\partial (ln(k))}{\partial P}=\frac{1}{k}\frac{\partial k}{\partial P}$

I am getting both of these terms from a paper on mineral physics and they seem to use both terms interchangeably. If so, how are these related?

 

[lurflurf]

log'(k)=1/k
So yes that is true except at zero or crossing branch cuts.

 

[dimension10]

According to the chain rule, yes