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

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