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

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