There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -60{x}^{3} + 936{x}^{2} - 4851x + 8349 - 3({(2x - 10)}^{\frac{1}{2}})(4{x}^{3} - 48{x}^{2} + 165x - 121)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -60x^{3} + 936x^{2} - 4851x - 12(2x - 10)^{\frac{1}{2}}x^{3} + 144(2x - 10)^{\frac{1}{2}}x^{2} - 495(2x - 10)^{\frac{1}{2}}x + 363(2x - 10)^{\frac{1}{2}} + 8349\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -60x^{3} + 936x^{2} - 4851x - 12(2x - 10)^{\frac{1}{2}}x^{3} + 144(2x - 10)^{\frac{1}{2}}x^{2} - 495(2x - 10)^{\frac{1}{2}}x + 363(2x - 10)^{\frac{1}{2}} + 8349\right)}{dx}\\=&-60*3x^{2} + 936*2x - 4851 - 12(\frac{\frac{1}{2}(2 + 0)}{(2x - 10)^{\frac{1}{2}}})x^{3} - 12(2x - 10)^{\frac{1}{2}}*3x^{2} + 144(\frac{\frac{1}{2}(2 + 0)}{(2x - 10)^{\frac{1}{2}}})x^{2} + 144(2x - 10)^{\frac{1}{2}}*2x - 495(\frac{\frac{1}{2}(2 + 0)}{(2x - 10)^{\frac{1}{2}}})x - 495(2x - 10)^{\frac{1}{2}} + 363(\frac{\frac{1}{2}(2 + 0)}{(2x - 10)^{\frac{1}{2}}}) + 0\\=&-180x^{2} + 1872x - \frac{12x^{3}}{(2x - 10)^{\frac{1}{2}}} - 36(2x - 10)^{\frac{1}{2}}x^{2} + \frac{144x^{2}}{(2x - 10)^{\frac{1}{2}}} + 288(2x - 10)^{\frac{1}{2}}x - \frac{495x}{(2x - 10)^{\frac{1}{2}}} - 495(2x - 10)^{\frac{1}{2}} + \frac{363}{(2x - 10)^{\frac{1}{2}}} - 4851\\ \end{split}\end{equation} \]

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