I am wondering how do the authors of this paper perform the following step (in the paper it is on page 29):
$$\dfrac{\partial L}{\partial \gamma_i}=\Psi^\prime(\gamma_i)\left(\alpha_i + \sum_{n=1}^N\phi_{ni}-\gamma_i\right)-\Psi^\prime\left(\sum_{j=1}^k\gamma_j\right)\sum_{j=1}^k\left(\alpha_j+\sum_{n=1}^N\phi_{nj}-\gamma_j\right)=0$$
Maximized for:
$$\gamma_i=\alpha_i+\sum_{n=1}^N\phi_{ni}$$
Does anyone know the calculations for this step? ($\Psi'$ is the derivative of the digamma function, everything else is a variable)
Just plugging the $\gamma_i$ and $\gamma_j$ into the second and fourth brackets turns those brackets into 0. And thus the expression into 0.