There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x{0}^{(-xx - 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x{0}^{(-x^{2} - 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{0}^{(-x^{2} - 1)}\right)}{dx}\\=&{0}^{(-x^{2} - 1)} + x({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))\\=&{0}^{(-x^{2} - 1)} - 2x^{2}{0}^{(-x^{2} - 1)}ln(0)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {0}^{(-x^{2} - 1)} - 2x^{2}{0}^{(-x^{2} - 1)}ln(0)\right)}{dx}\\=&({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)})) - 2*2x{0}^{(-x^{2} - 1)}ln(0) - 2x^{2}({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln(0) - \frac{2x^{2}{0}^{(-x^{2} - 1)}*0}{(0)}\\=&-6x{0}^{(-x^{2} - 1)}ln(0) + 4x^{3}{0}^{(-x^{2} - 1)}ln^{2}(0)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -6x{0}^{(-x^{2} - 1)}ln(0) + 4x^{3}{0}^{(-x^{2} - 1)}ln^{2}(0)\right)}{dx}\\=&-6 * {0}^{(-x^{2} - 1)}ln(0) - 6x({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln(0) - \frac{6x{0}^{(-x^{2} - 1)}*0}{(0)} + 4*3x^{2}{0}^{(-x^{2} - 1)}ln^{2}(0) + 4x^{3}({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln^{2}(0) + \frac{4x^{3}{0}^{(-x^{2} - 1)}*2ln(0)*0}{(0)}\\=&-6 * {0}^{(-x^{2} - 1)}ln(0) + 24x^{2}{0}^{(-x^{2} - 1)}ln^{2}(0) - 8x^{4}{0}^{(-x^{2} - 1)}ln^{3}(0)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -6 * {0}^{(-x^{2} - 1)}ln(0) + 24x^{2}{0}^{(-x^{2} - 1)}ln^{2}(0) - 8x^{4}{0}^{(-x^{2} - 1)}ln^{3}(0)\right)}{dx}\\=&-6({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln(0) - \frac{6 * {0}^{(-x^{2} - 1)}*0}{(0)} + 24*2x{0}^{(-x^{2} - 1)}ln^{2}(0) + 24x^{2}({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln^{2}(0) + \frac{24x^{2}{0}^{(-x^{2} - 1)}*2ln(0)*0}{(0)} - 8*4x^{3}{0}^{(-x^{2} - 1)}ln^{3}(0) - 8x^{4}({0}^{(-x^{2} - 1)}((-2x + 0)ln(0) + \frac{(-x^{2} - 1)(0)}{(0)}))ln^{3}(0) - \frac{8x^{4}{0}^{(-x^{2} - 1)}*3ln^{2}(0)*0}{(0)}\\=&60x{0}^{(-x^{2} - 1)}ln^{2}(0) - 80x^{3}{0}^{(-x^{2} - 1)}ln^{3}(0) + 16x^{5}{0}^{(-x^{2} - 1)}ln^{4}(0)\\ \end{split}\end{equation} \]

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