There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (sqrt(1 + x) - 1)(sqrt(1 - x) - 1)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(x + 1)sqrt(-x + 1) - sqrt(x + 1) - sqrt(-x + 1) + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(x + 1)sqrt(-x + 1) - sqrt(x + 1) - sqrt(-x + 1) + 1\right)}{dx}\\=&\frac{(1 + 0)*\frac{1}{2}sqrt(-x + 1)}{(x + 1)^{\frac{1}{2}}} + \frac{sqrt(x + 1)(-1 + 0)*\frac{1}{2}}{(-x + 1)^{\frac{1}{2}}} - \frac{(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}} - \frac{(-1 + 0)*\frac{1}{2}}{(-x + 1)^{\frac{1}{2}}} + 0\\=&\frac{sqrt(-x + 1)}{2(x + 1)^{\frac{1}{2}}} - \frac{sqrt(x + 1)}{2(-x + 1)^{\frac{1}{2}}} - \frac{1}{2(x + 1)^{\frac{1}{2}}} + \frac{1}{2(-x + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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