There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(\frac{204}{5} - 4x)xsqrt(x + 1)}{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{34}{5}xsqrt(x + 1) - \frac{2}{3}x^{2}sqrt(x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{34}{5}xsqrt(x + 1) - \frac{2}{3}x^{2}sqrt(x + 1)\right)}{dx}\\=&\frac{34}{5}sqrt(x + 1) + \frac{\frac{34}{5}x(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}} - \frac{2}{3}*2xsqrt(x + 1) - \frac{\frac{2}{3}x^{2}(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}}\\=&\frac{34sqrt(x + 1)}{5} + \frac{17x}{5(x + 1)^{\frac{1}{2}}} - \frac{4xsqrt(x + 1)}{3} - \frac{x^{2}}{3(x + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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