Why does $\frac{d}{d\theta} \theta\prod_{i=1}^nx_i = \sum_{i=1}^nx_i$

Why does $\frac{d}{d\theta} \theta\prod_{i=1}^nx_i = \sum_{i=1}^nx_i$

Is this just the product rule? I have this in my notes but I didn't think
anything of it and now I'm wondering how this happens?
Edit: Im working with maximum likelihood estimation and in my notes I have
that the likelihood funciton $=L(x;\theta)=\prod_{i=1}^nf(x;\theta)$ where
$x$ is the variable and $\theta$ is the parameter of a probability
distribution. To estimate I was told that we take the log of the
likelihood function e.i. $ln(L)$, then take it's derivative to estimate
the parameter. The function I'm working with is $f(x;\theta)=(\theta
+1)x^{\theta}$. So $$L(x;\theta)=\prod_{i=1}^n(\theta
+1)x_i^{\theta}=(\theta+1)^n\prod_{i=1}^nx_i^{\theta}$$ Now
$$ln(L(x;\theta))=n*ln(\theta+1)+\theta
ln\left(\prod_{i=1}^nx_i\right)$$Here's where I'm confused, I have in my
notes that $$\frac{dL}{d\theta}=\frac{n}{\theta+1}+\sum_{i=1}^nln(x_i)$$
Why does the product of $x_i$ become the summation of $x_i$?