Derivative of $\frac{d}{d\theta }\left(\left(\theta \:-1\right)\sum\limits_{i=0}^n\:\ln\left(x_i\right)\right)$

Question

I'm doing some maximum likelihood estimation exercise and I got stuck on the derivative of the following part: $\frac{d}{d\theta }\left(\left(\theta \:-1\right)\sum\limits_{i=0}^n\:\ln\left(x_i\right)\right)$

Answer 1

The sum is a constant with respect to $\theta$. So the answer is $$\sum\limits_{i}\ln x_i,$$ since $\frac{d}{d\theta}((\theta-1)c)=c$ if $c$ is a constant.