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

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