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

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