Mean Occupation Number of Non-interacting quantum fluids

[unscientific]

Hi, I get two contradicting sections of the book "Concepts in Thermal Physics":

Earlier in the section they used the grand partition function to derive the mean occupation number $<n_i> = -\frac{1}{\beta}\frac{\partial ln Z}{\partial E_i}$

Later in the section, they said $<n_k> = \frac{1}{\beta}\frac{\partial Z_k}{\partial \mu}$

Why does the first expression take the differential of $ln Z$ and the second expression simply takes the differential of $Z$?

 

[unscientific]

If it helps, it was earlier defined that $Z = \Pi_i\left( 1 \pm e^{\beta(\mu - E_i)}\right)^{\pm 1}$

 

[unscientific]

bumpp

 

[Hypersphere]

It should be ln Z, it's just an error in the book. And the author is aware of it already, see this errata.