There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(sqrt(x + 1))({(3 - x)}^{3})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -x^{3}ln(sqrt(x + 1)) + 9x^{2}ln(sqrt(x + 1)) - 27xln(sqrt(x + 1)) + 27ln(sqrt(x + 1))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -x^{3}ln(sqrt(x + 1)) + 9x^{2}ln(sqrt(x + 1)) - 27xln(sqrt(x + 1)) + 27ln(sqrt(x + 1))\right)}{dx}\\=&-3x^{2}ln(sqrt(x + 1)) - \frac{x^{3}(1 + 0)*\frac{1}{2}}{(sqrt(x + 1))(x + 1)^{\frac{1}{2}}} + 9*2xln(sqrt(x + 1)) + \frac{9x^{2}(1 + 0)*\frac{1}{2}}{(sqrt(x + 1))(x + 1)^{\frac{1}{2}}} - 27ln(sqrt(x + 1)) - \frac{27x(1 + 0)*\frac{1}{2}}{(sqrt(x + 1))(x + 1)^{\frac{1}{2}}} + \frac{27(1 + 0)*\frac{1}{2}}{(sqrt(x + 1))(x + 1)^{\frac{1}{2}}}\\=&-3x^{2}ln(sqrt(x + 1)) - \frac{x^{3}}{2(x + 1)^{\frac{1}{2}}sqrt(x + 1)} + 18xln(sqrt(x + 1)) + \frac{9x^{2}}{2(x + 1)^{\frac{1}{2}}sqrt(x + 1)} - 27ln(sqrt(x + 1)) - \frac{27x}{2(x + 1)^{\frac{1}{2}}sqrt(x + 1)} + \frac{27}{2(x + 1)^{\frac{1}{2}}sqrt(x + 1)}\\ \end{split}\end{equation} \]

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