There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ ln(x){x}^{log_{2}^{x}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{log_{2}^{x}}ln(x)\\\\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&\frac{24{x}^{log_{2}^{x}}ln(x)ln(x)}{x^{5}ln(2)} + \frac{36{x}^{log_{2}^{x}}ln(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{90{x}^{log_{2}^{x}}ln^{2}(x)ln(x)}{x^{5}ln^{3}(2)} + \frac{24{x}^{log_{2}^{x}}ln(x)ln(x)}{x^{5}ln^{3}(2)} + \frac{140{x}^{log_{2}^{x}}ln(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{16{x}^{log_{2}^{x}}ln^{3}(x)ln(x)}{x^{5}ln^{4}(2)} - \frac{50{x}^{log_{2}^{x}}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{70{x}^{log_{2}^{x}}ln(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{35{x}^{log_{2}^{x}}ln^{3}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{30{x}^{log_{2}^{x}}ln^{2}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{10{x}^{log_{2}^{x}}ln^{4}(x)ln(x)}{x^{5}ln^{4}(2)} + \frac{4{x}^{log_{2}^{x}}ln^{3}(x)ln(x)}{x^{5}ln^{4}(2)} + \frac{{x}^{log_{2}^{x}}ln^{5}(x)ln(x)}{x^{5}ln^{5}(2)} + \frac{35{x}^{log_{2}^{x}}ln^{2}(x)}{x^{5}ln^{2}(2)} - \frac{140{x}^{log_{2}^{x}}ln(x)}{x^{5}ln^{2}(2)} - \frac{100{x}^{log_{2}^{x}}ln(x)}{x^{5}ln(2)} - \frac{120{x}^{log_{2}^{x}}ln(x)}{x^{5}ln^{2}(2)} - \frac{10{x}^{log_{2}^{x}}ln^{3}(x)}{x^{5}ln^{3}(2)} + \frac{39{x}^{log_{2}^{x}}ln^{2}(x)}{x^{5}ln^{3}(2)} - \frac{100{x}^{log_{2}^{x}}ln(x)}{x^{5}ln^{2}(2)} + \frac{21{x}^{log_{2}^{x}}ln^{2}(x)}{x^{5}ln^{3}(2)} + \frac{{x}^{log_{2}^{x}}log_{2}^{x}ln^{4}(x)ln(x)}{x^{5}ln^{4}(2)} - \frac{100{x}^{log_{2}^{x}}ln(x)}{x^{5}ln(2)} + \frac{{x}^{log_{2}^{x}}ln^{4}(x)}{x^{5}ln^{4}(2)} - \frac{100{x}^{log_{2}^{x}}log_{2}^{x}ln(x)ln(x)}{x^{5}ln(2)} + \frac{70{x}^{log_{2}^{x}}ln^{2}(x)}{x^{5}ln^{2}(2)} + \frac{21{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{140{x}^{log_{2}^{x}}log_{2}^{x}ln(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{39{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)ln(x)}{x^{5}ln^{3}(2)} + \frac{38{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)ln(x)}{x^{5}ln^{2}(2)} - \frac{100{x}^{log_{2}^{x}}log_{2}^{x}ln(x)ln(x)}{x^{5}ln^{2}(2)} - \frac{10{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)ln(x)}{x^{5}ln^{3}(2)} + \frac{35{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} - \frac{30{x}^{log_{2}^{x}}ln^{3}(x)}{x^{5}ln^{3}(2)} + \frac{4{x}^{log_{2}^{x}}log_{2}^{x}ln^{4}(x)ln(x)}{x^{5}ln^{4}(2)} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{3}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{30{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{10{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{70{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{105{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)ln(x)}{x^{5}ln(2)} + \frac{4{x}^{log_{2}^{x}}ln^{4}(x)}{x^{5}ln^{4}(2)} - \frac{50{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{9{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{3}(x)ln(x)}{x^{5}ln^{3}(2)} - \frac{40{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)ln(x)}{x^{5}ln(2)} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{22{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{9{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln^{2}(x)ln(x)}{x^{5}ln^{2}(2)} + \frac{5{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{4}ln(x)ln(x)}{x^{5}ln(2)} + \frac{140{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln(2)} + \frac{60{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln^{2}(2)} + \frac{68{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln^{2}(2)} + \frac{52{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln^{2}(2)} - \frac{80{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{5}ln^{2}(2)} - \frac{40{x}^{log_{2}^{x}}log_{2}^{x}ln^{2}(x)}{x^{5}ln^{2}(2)} - \frac{120{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{5}ln(2)} - \frac{70{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{5}ln(2)} + \frac{14{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{5}ln^{3}(2)} + \frac{210{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln(2)} + \frac{9{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{5}ln^{2}(2)} + \frac{6{x}^{log_{2}^{x}}log_{2}^{x}ln^{3}(x)}{x^{5}ln^{3}(2)} + \frac{21{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln^{2}(x)}{x^{5}ln^{2}(2)} + \frac{20{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{5}ln(2)} + \frac{11{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{5}ln(2)} + \frac{70{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}ln(2)} + \frac{210{x}^{log_{2}^{x}}}{x^{5}ln(2)} - \frac{50{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{5}ln(2)} + \frac{60{x}^{log_{2}^{x}}}{x^{5}ln^{2}(2)} + \frac{9{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{5}ln(2)} + \frac{60{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{5}ln(2)} - \frac{240{x}^{log_{2}^{x}}log_{2}^{x}}{x^{5}ln(2)} - \frac{50{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}ln(x)}{x^{5}} + \frac{35{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}ln(x)}{x^{5}} + \frac{24{x}^{log_{2}^{x}}log_{2}^{x}ln(x)}{x^{5}} - \frac{10{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{4}ln(x)}{x^{5}} + \frac{{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{5}ln(x)}{x^{5}} - \frac{100{x}^{log_{2}^{x}}log_{2}^{x}}{x^{5}} - \frac{40{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{3}}{x^{5}} + \frac{105{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{2}}{x^{5}} + \frac{5{x}^{log_{2}^{x}}{\left(log_{2}^{x}\right)}^{4}}{x^{5}} + \frac{24{x}^{log_{2}^{x}}}{x^{5}}\\ \end{split}\end{equation} \]

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