There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sqrt(2)x)}{(4sqrt(\frac{{x}^{2}}{4} + 900))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{4}xsqrt(2)}{sqrt(\frac{1}{4}x^{2} + 900)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{4}xsqrt(2)}{sqrt(\frac{1}{4}x^{2} + 900)}\right)}{dx}\\=&\frac{\frac{1}{4}sqrt(2)}{sqrt(\frac{1}{4}x^{2} + 900)} + \frac{\frac{1}{4}x*0*\frac{1}{2}*2^{\frac{1}{2}}}{sqrt(\frac{1}{4}x^{2} + 900)} + \frac{\frac{1}{4}xsqrt(2)*-(\frac{1}{4}*2x + 0)*\frac{1}{2}}{(\frac{1}{4}x^{2} + 900)(\frac{1}{4}x^{2} + 900)^{\frac{1}{2}}}\\=&\frac{sqrt(2)}{4sqrt(\frac{1}{4}x^{2} + 900)} - \frac{x^{2}sqrt(2)}{16(\frac{1}{4}x^{2} + 900)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

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