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

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