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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{0.0015}{(1 + \frac{x}{10000})} + (-0.000942)e^{\frac{1500}{x}}{(1 - e^{\frac{-1500}{x}})}^{2.5}{(\frac{1500}{x})}^{-0.5} + \frac{(-0.0004882)*1500}{x} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = -0.0000243223354(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}x^{\frac{1}{2}}e^{\frac{1500}{x}} + \frac{0.0015}{(0.0001x + 1)} - \frac{0.7323}{x}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( -0.0000243223354(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}x^{\frac{1}{2}}e^{\frac{1500}{x}} + \frac{0.0015}{(0.0001x + 1)} - \frac{0.7323}{x}\right)}{dx}\\=&-0.0000243223354(2.5(-e^{\frac{-1500}{x}} + 1)^{\frac{3}{2}}(\frac{-e^{\frac{-1500}{x}}*-1500*-1}{x^{2}} + 0))x^{\frac{1}{2}}e^{\frac{1500}{x}} - \frac{0.0000243223354141826(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}*0.5e^{\frac{1500}{x}}}{x^{\frac{1}{2}}} - \frac{0.0000243223354141826(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}x^{\frac{1}{2}}e^{\frac{1500}{x}}*1500*-1}{x^{2}} + 0.0015(\frac{-(0.0001 + 0)}{(0.0001x + 1)^{2}}) - \frac{0.7323*-1}{x^{2}}\\=&\frac{0.0912087578031847(-e^{\frac{-1500}{x}} + 1)^{\frac{3}{2}}e^{\frac{-1500}{x}}e^{\frac{1500}{x}}}{x^{\frac{3}{2}}} - \frac{0.0000121611677070913(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}e^{\frac{1500}{x}}}{x^{\frac{1}{2}}} + \frac{0.0364835031212739(-e^{\frac{-1500}{x}} + 1)^{\frac{5}{2}}e^{\frac{1500}{x}}}{x^{\frac{3}{2}}} - \frac{0.00000015}{(0.0001x + 1)(0.0001x + 1)} + \frac{0.7323}{x^{2}}\\ \end{split}\end{equation} \]

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