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

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