There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ({a}^{x} - 1 - x){\frac{1}{x}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{a}^{x}}{x^{2}} - \frac{1}{x} - \frac{1}{x^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{a}^{x}}{x^{2}} - \frac{1}{x} - \frac{1}{x^{2}}\right)}{dx}\\=&\frac{-2{a}^{x}}{x^{3}} + \frac{({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))}{x^{2}} - \frac{-1}{x^{2}} - \frac{-2}{x^{3}}\\=&\frac{{a}^{x}ln(a)}{x^{2}} - \frac{2{a}^{x}}{x^{3}} + \frac{1}{x^{2}} + \frac{2}{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{a}^{x}ln(a)}{x^{2}} - \frac{2{a}^{x}}{x^{3}} + \frac{1}{x^{2}} + \frac{2}{x^{3}}\right)}{dx}\\=&\frac{-2{a}^{x}ln(a)}{x^{3}} + \frac{({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln(a)}{x^{2}} + \frac{{a}^{x}*0}{x^{2}(a)} - \frac{2*-3{a}^{x}}{x^{4}} - \frac{2({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))}{x^{3}} + \frac{-2}{x^{3}} + \frac{2*-3}{x^{4}}\\=&\frac{-4{a}^{x}ln(a)}{x^{3}} + \frac{{a}^{x}ln^{2}(a)}{x^{2}} + \frac{6{a}^{x}}{x^{4}} - \frac{2}{x^{3}} - \frac{6}{x^{4}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-4{a}^{x}ln(a)}{x^{3}} + \frac{{a}^{x}ln^{2}(a)}{x^{2}} + \frac{6{a}^{x}}{x^{4}} - \frac{2}{x^{3}} - \frac{6}{x^{4}}\right)}{dx}\\=&\frac{-4*-3{a}^{x}ln(a)}{x^{4}} - \frac{4({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln(a)}{x^{3}} - \frac{4{a}^{x}*0}{x^{3}(a)} + \frac{-2{a}^{x}ln^{2}(a)}{x^{3}} + \frac{({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln^{2}(a)}{x^{2}} + \frac{{a}^{x}*2ln(a)*0}{x^{2}(a)} + \frac{6*-4{a}^{x}}{x^{5}} + \frac{6({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))}{x^{4}} - \frac{2*-3}{x^{4}} - \frac{6*-4}{x^{5}}\\=&\frac{18{a}^{x}ln(a)}{x^{4}} - \frac{6{a}^{x}ln^{2}(a)}{x^{3}} + \frac{{a}^{x}ln^{3}(a)}{x^{2}} - \frac{24{a}^{x}}{x^{5}} + \frac{6}{x^{4}} + \frac{24}{x^{5}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{18{a}^{x}ln(a)}{x^{4}} - \frac{6{a}^{x}ln^{2}(a)}{x^{3}} + \frac{{a}^{x}ln^{3}(a)}{x^{2}} - \frac{24{a}^{x}}{x^{5}} + \frac{6}{x^{4}} + \frac{24}{x^{5}}\right)}{dx}\\=&\frac{18*-4{a}^{x}ln(a)}{x^{5}} + \frac{18({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln(a)}{x^{4}} + \frac{18{a}^{x}*0}{x^{4}(a)} - \frac{6*-3{a}^{x}ln^{2}(a)}{x^{4}} - \frac{6({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln^{2}(a)}{x^{3}} - \frac{6{a}^{x}*2ln(a)*0}{x^{3}(a)} + \frac{-2{a}^{x}ln^{3}(a)}{x^{3}} + \frac{({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))ln^{3}(a)}{x^{2}} + \frac{{a}^{x}*3ln^{2}(a)*0}{x^{2}(a)} - \frac{24*-5{a}^{x}}{x^{6}} - \frac{24({a}^{x}((1)ln(a) + \frac{(x)(0)}{(a)}))}{x^{5}} + \frac{6*-4}{x^{5}} + \frac{24*-5}{x^{6}}\\=&\frac{-96{a}^{x}ln(a)}{x^{5}} + \frac{36{a}^{x}ln^{2}(a)}{x^{4}} - \frac{8{a}^{x}ln^{3}(a)}{x^{3}} + \frac{{a}^{x}ln^{4}(a)}{x^{2}} + \frac{120{a}^{x}}{x^{6}} - \frac{24}{x^{5}} - \frac{120}{x^{6}}\\ \end{split}\end{equation} \]

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