求助啊,李航的最大熵推导是怎么推的?

$\begin{aligned} L(P, w) & \equiv-H(P)+w_{0}\left(1-\sum_{y} P(y | x)\right)+\sum_{i=1}^{n} w_{i}\left(E_{\overline{p}}\left(f_{i}\right)-E_{P}\left(f_{i}\right)\right) \\=& {\color{red}\sum_{x, y} \tilde{P}(x) P(y | x) \log P(y | x) } +{\color{blue} w_{0}\left(1-\sum_{y} P(y | x)\right)} \\ &+\sum_{i=1}^{n} w_{i}\left(\sum_{x, y} \tilde{P}(x, y) f_{i}(x, y)-\sum_{x, y} \tilde{P}(x) P(y | x) f_{i}(x, y)\right) \end{aligned}$

$L(P, w)$对P(y|x)求导 假如是对 $P(y_1|x_1)$求导,如下

$\frac{\partial L(P,W)}{\partial P(y_1|x_1)}={\color{red}\tilde {P}(x_1)(logP(y_1|x_1)+1)}{\color{blue}-w_0}+\sum_{i=1}^nw_i\sum_{x,y}\tilde P(x)P(y|x)f_i(x,y)$

其中红色部分是因为只有 $x=x_1,y=y_1$那一项才含有 $P(y_1|x_1)$

应用 $\sum_x\tilde P(x)=1$
$=\tilde{P}(x_1)(logP(y_1|x_1)+1) +\sum_x\tilde P(x)w_0+\sum_{x,y}\tilde P(x)\sum_{i=1}^nw_iP(y|x)f_i(x,y)$

问题是最后怎么推出
$\sum_{x, y} \tilde{P}(x)\left(\log P(y | x)+1-w_{0}-\sum_{i=1}^{n} w_{i} f_{i}(x, y)\right)$
的???