There are 1 questions in this calculation: for each question, the 1 derivative of a is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -aln(a) - bln(b) - (1 - a - b)ln(1 - a - b)\ with\ respect\ to\ a：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -aln(a) - bln(b) - ln(-a - b + 1) + aln(-a - b + 1) + bln(-a - b + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -aln(a) - bln(b) - ln(-a - b + 1) + aln(-a - b + 1) + bln(-a - b + 1)\right)}{da}\\=&-ln(a) - \frac{a}{(a)} - \frac{b*0}{(b)} - \frac{(-1 + 0 + 0)}{(-a - b + 1)} + ln(-a - b + 1) + \frac{a(-1 + 0 + 0)}{(-a - b + 1)} + \frac{b(-1 + 0 + 0)}{(-a - b + 1)}\\=&-ln(a) - \frac{a}{(-a - b + 1)} + ln(-a - b + 1) - \frac{b}{(-a - b + 1)} + \frac{1}{(-a - b + 1)} - 1\\ \end{split}\end{equation} \]

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