本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数xln(x + sqrt({x}^{2} - {a}^{2})) - sqrt({x}^{2} - {a}^{2}) 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = xln(x + sqrt(x^{2} - a^{2})) - sqrt(x^{2} - a^{2})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( xln(x + sqrt(x^{2} - a^{2})) - sqrt(x^{2} - a^{2})\right)}{dx}\\=&ln(x + sqrt(x^{2} - a^{2})) + \frac{x(1 + \frac{(2x + 0)*\frac{1}{2}}{(x^{2} - a^{2})^{\frac{1}{2}}})}{(x + sqrt(x^{2} - a^{2}))} - \frac{(2x + 0)*\frac{1}{2}}{(x^{2} - a^{2})^{\frac{1}{2}}}\\=&ln(x + sqrt(x^{2} - a^{2})) + \frac{x}{(x + sqrt(x^{2} - a^{2}))} + \frac{x^{2}}{(x + sqrt(x^{2} - a^{2}))(x^{2} - a^{2})^{\frac{1}{2}}} - \frac{x}{(x^{2} - a^{2})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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