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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{-(40sqrt(7 - 4sin(x))sin(x)sqrt(4sin(x) + 7) + 160cos(x)sin(x))}{(sqrt(7 - 4sin(x))sqrt(4sin(x) + 7))} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{160sin(x)cos(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} - 40sin(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( - \frac{160sin(x)cos(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} - 40sin(x)\right)}{dx}\\=& - \frac{160cos(x)cos(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} - \frac{160sin(x)*-sin(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} - \frac{160sin(x)cos(x)*-(-4cos(x) + 0)*\frac{1}{2}}{(-4sin(x) + 7)(-4sin(x) + 7)^{\frac{1}{2}}sqrt(4sin(x) + 7)} - \frac{160sin(x)cos(x)*-(4cos(x) + 0)*\frac{1}{2}}{sqrt(-4sin(x) + 7)(4sin(x) + 7)(4sin(x) + 7)^{\frac{1}{2}}} - 40cos(x)\\=& - \frac{160cos^{2}(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} + \frac{160sin^{2}(x)}{sqrt(-4sin(x) + 7)sqrt(4sin(x) + 7)} - \frac{320sin(x)cos^{2}(x)}{(-4sin(x) + 7)^{\frac{3}{2}}sqrt(4sin(x) + 7)} + \frac{320sin(x)cos^{2}(x)}{(4sin(x) + 7)^{\frac{3}{2}}sqrt(-4sin(x) + 7)} - 40cos(x)\\ \end{split}\end{equation} \]

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