There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sqrt(3sqrt({x}^{5}) + 7{x}^{2} - 14))}{(2{x}^{0.76})} + {x}^{-1}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{0.5sqrt(3sqrt(x^{5}) + 7x^{2} - 14)}{x^{\frac{19}{25}}} + \frac{1}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{0.5sqrt(3sqrt(x^{5}) + 7x^{2} - 14)}{x^{\frac{19}{25}}} + \frac{1}{x}\right)}{dx}\\=&\frac{0.5*-0.76sqrt(3sqrt(x^{5}) + 7x^{2} - 14)}{x^{\frac{44}{25}}} + \frac{0.5(3*5x^{4}*0.5x^{\frac{5}{2}} + 7*2x + 0)*0.5}{x^{\frac{19}{25}}(3sqrt(x^{5}) + 7x^{2} - 14)^{\frac{1}{2}}} - \frac{1}{x^{2}}\\=&\frac{-0.38sqrt(3sqrt(x^{5}) + 7x^{2} - 14)}{x^{\frac{44}{25}}} + \frac{1.875x^{\frac{287}{50}}}{(3sqrt(x^{5}) + 7x^{2} - 14)^{\frac{1}{2}}} + \frac{3.5x^{\frac{6}{25}}}{(3sqrt(x^{5}) + 7x^{2} - 14)^{\frac{1}{2}}} - \frac{1}{x^{2}}\\ \end{split}\end{equation} \]

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