We can rewrite
$$ \nabla_{\boldsymbol{\Theta}}\log{Z(\boldsymbol{\Theta})}=\frac{\nabla_{\boldsymbol{\Theta}}Z(\boldsymbol{\Theta})}{Z(\boldsymbol{\Theta})}, $$which reads in more detail
$$ \nabla_{\boldsymbol{\Theta}}\log{Z(\boldsymbol{\Theta})}=\frac{\nabla_{\boldsymbol{\Theta}} \sum_{x_i\in \boldsymbol{X}}f(x_i;\boldsymbol{\Theta}) }{Z(\boldsymbol{\Theta})}. $$We can rewrite the function \( f \) (we have assumed that is larger or equal than zero) as \( f=\exp{\log{f}} \). We can then reqrite the last equation as
$$ \nabla_{\boldsymbol{\Theta}}\log{Z(\boldsymbol{\Theta})}=\frac{ \sum_{x_i\in \boldsymbol{X}} \nabla_{\boldsymbol{\Theta}}\exp{\log{f(x_i;\boldsymbol{\Theta})}} }{Z(\boldsymbol{\Theta})}. $$