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

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