There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (\frac{sqrt(2)}{3})ln((sqrt(2)x - \frac{(\frac{sqrt(2)}{2})x}{sqrt(2)} + sqrt(2)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{3}ln(xsqrt(2) - \frac{1}{2}x + sqrt(2))sqrt(2)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{3}ln(xsqrt(2) - \frac{1}{2}x + sqrt(2))sqrt(2)\right)}{dx}\\=&\frac{\frac{1}{3}(sqrt(2) + x*0*\frac{1}{2}*2^{\frac{1}{2}} - \frac{1}{2} + 0*\frac{1}{2}*2^{\frac{1}{2}})sqrt(2)}{(xsqrt(2) - \frac{1}{2}x + sqrt(2))} + \frac{1}{3}ln(xsqrt(2) - \frac{1}{2}x + sqrt(2))*0*\frac{1}{2}*2^{\frac{1}{2}}\\=&\frac{sqrt(2)^{2}}{3(xsqrt(2) - \frac{1}{2}x + sqrt(2))} - \frac{sqrt(2)}{6(xsqrt(2) - \frac{1}{2}x + sqrt(2))}\\ \end{split}\end{equation} \]

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