There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ((1 - {x}^{100}){(1 - (sqrt(x)))}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -x^{100}sqrt(x)^{2} + 2x^{100}sqrt(x) - x^{100} + sqrt(x)^{2} - 2sqrt(x) + 1\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -x^{100}sqrt(x)^{2} + 2x^{100}sqrt(x) - x^{100} + sqrt(x)^{2} - 2sqrt(x) + 1\right)}{dx}\\=&-100x^{99}sqrt(x)^{2} - \frac{x^{100}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 2*100x^{99}sqrt(x) + \frac{2x^{100}*\frac{1}{2}}{(x)^{\frac{1}{2}}} - 100x^{99} + \frac{2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} - \frac{2*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 0\\=&-100x^{99}sqrt(x)^{2} + 200x^{99}sqrt(x) - x^{100} + x^{\frac{199}{2}} - 100x^{99} - \frac{1}{x^{\frac{1}{2}}} + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -100x^{99}sqrt(x)^{2} + 200x^{99}sqrt(x) - x^{100} + x^{\frac{199}{2}} - 100x^{99} - \frac{1}{x^{\frac{1}{2}}} + 1\right)}{dx}\\=&-100*99x^{98}sqrt(x)^{2} - \frac{100x^{99}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 200*99x^{98}sqrt(x) + \frac{200x^{99}*\frac{1}{2}}{(x)^{\frac{1}{2}}} - 100x^{99} + \frac{199}{2}x^{\frac{197}{2}} - 100*99x^{98} - \frac{\frac{-1}{2}}{x^{\frac{3}{2}}} + 0\\=&-9900x^{98}sqrt(x)^{2} + 19800x^{98}sqrt(x) - 200x^{99} + \frac{399x^{\frac{197}{2}}}{2} - 9900x^{98} + \frac{1}{2x^{\frac{3}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -9900x^{98}sqrt(x)^{2} + 19800x^{98}sqrt(x) - 200x^{99} + \frac{399x^{\frac{197}{2}}}{2} - 9900x^{98} + \frac{1}{2x^{\frac{3}{2}}}\right)}{dx}\\=&-9900*98x^{97}sqrt(x)^{2} - \frac{9900x^{98}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 19800*98x^{97}sqrt(x) + \frac{19800x^{98}*\frac{1}{2}}{(x)^{\frac{1}{2}}} - 200*99x^{98} + \frac{399*\frac{197}{2}x^{\frac{195}{2}}}{2} - 9900*98x^{97} + \frac{\frac{-3}{2}}{2x^{\frac{5}{2}}}\\=&-970200x^{97}sqrt(x)^{2} + 1940400x^{97}sqrt(x) - 29700x^{98} + \frac{118203x^{\frac{195}{2}}}{4} - 970200x^{97} - \frac{3}{4x^{\frac{5}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( -970200x^{97}sqrt(x)^{2} + 1940400x^{97}sqrt(x) - 29700x^{98} + \frac{118203x^{\frac{195}{2}}}{4} - 970200x^{97} - \frac{3}{4x^{\frac{5}{2}}}\right)}{dx}\\=&-970200*97x^{96}sqrt(x)^{2} - \frac{970200x^{97}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 1940400*97x^{96}sqrt(x) + \frac{1940400x^{97}*\frac{1}{2}}{(x)^{\frac{1}{2}}} - 29700*98x^{97} + \frac{118203*\frac{195}{2}x^{\frac{193}{2}}}{4} - 970200*97x^{96} - \frac{3*\frac{-5}{2}}{4x^{\frac{7}{2}}}\\=&-94109400x^{96}sqrt(x)^{2} + 188218800x^{96}sqrt(x) - 3880800x^{97} + \frac{30811185x^{\frac{193}{2}}}{8} - 94109400x^{96} + \frac{15}{8x^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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