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

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