There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{ln(sqrt(1 - x)){e}^{x}}{sqrt(arccos(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{x}ln(sqrt(-x + 1))}{sqrt(arccos(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{e}^{x}ln(sqrt(-x + 1))}{sqrt(arccos(x))}\right)}{dx}\\=&\frac{({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))ln(sqrt(-x + 1))}{sqrt(arccos(x))} + \frac{{e}^{x}(-1 + 0)*\frac{1}{2}}{(sqrt(-x + 1))(-x + 1)^{\frac{1}{2}}sqrt(arccos(x))} + \frac{{e}^{x}ln(sqrt(-x + 1))*-(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})*\frac{1}{2}}{(arccos(x))(arccos(x))^{\frac{1}{2}}}\\=&\frac{{e}^{x}ln(sqrt(-x + 1))}{sqrt(arccos(x))} - \frac{{e}^{x}}{2(-x + 1)^{\frac{1}{2}}sqrt(-x + 1)sqrt(arccos(x))} + \frac{{e}^{x}ln(sqrt(-x + 1))}{2(-x^{2} + 1)^{\frac{1}{2}}arccos^{\frac{3}{2}}(x)}\\ \end{split}\end{equation} \]

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