Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
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There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {(x - 1)}^{e^{x}}m({x}^{2} + 3)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = mx^{2}(x - 1)^{e^{x}} + 3m(x - 1)^{e^{x}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( mx^{2}(x - 1)^{e^{x}} + 3m(x - 1)^{e^{x}}\right)}{dx}\\=&m*2x(x - 1)^{e^{x}} + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)})) + 3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))\\=&mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + 2mx(x - 1)^{e^{x}} + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + 2mx(x - 1)^{e^{x}} + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)}\right)}{dx}\\=&m*2x(x - 1)^{e^{x}}e^{x}ln(x - 1) + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 2m(x - 1)^{e^{x}} + 2mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)})) + (\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{x} + \frac{m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 3(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{x} + \frac{3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)}\\=&4mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{2mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) - \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{4mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + 3m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{6m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + 2m(x - 1)^{e^{x}} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)} - \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{3m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 4mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{2mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) - \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{4mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + 3m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{6m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + 2m(x - 1)^{e^{x}} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)} - \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{3m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}}\right)}{dx}\\=&4m(x - 1)^{e^{x}}e^{x}ln(x - 1) + 4mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + 4mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{4mx(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + m*2x(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln^{2}(x - 1) + mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}ln^{2}(x - 1) + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}*2ln(x - 1)(1 + 0)}{(x - 1)} + 2(\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) + \frac{2m*2x(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{2mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{2mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)} + \frac{2mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)(x - 1)} + m*2x(x - 1)^{e^{x}}e^{x}ln(x - 1) + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 2(\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{x} + \frac{2m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{2mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + 3m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} - (\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{x} - \frac{m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{2}} - \frac{mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 4(\frac{-(1 + 0)}{(x - 1)^{2}})mx(x - 1)^{e^{x}}e^{x} + \frac{4m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{4mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{4mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + (\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}} + \frac{m*2x(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{2}} + \frac{mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{2}} + 3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln^{2}(x - 1) + 3m(x - 1)^{e^{x}}*2e^{x}e^{x}ln^{2}(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{{x}*{2}}*2ln(x - 1)(1 + 0)}{(x - 1)} + 6(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) + \frac{6m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{6m(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)} + \frac{6m(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)(x - 1)} + 2m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)})) + 6(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{x} + \frac{6m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)} - 3(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{x} - \frac{3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{2}} - \frac{3m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 3(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{{x}*{2}} + \frac{3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{2}} + \frac{3m(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{2}}\\=&9m(x - 1)^{e^{x}}e^{x}ln(x - 1) + 6mx(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + 6mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{12mx(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + 3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{9mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{12mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{6mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 9m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{27m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - \frac{6mx(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 3m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + \frac{6mx(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{15m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{18m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{3m(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 9m(x - 1)^{e^{x}}e^{x}ln(x - 1) + 6mx(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + 6mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{12mx(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + 3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{9mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{12mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{6mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 9m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{27m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - \frac{6mx(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 3m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + \frac{6mx(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{15m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{18m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{3m(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}}\right)}{dx}\\=&9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + 9m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{9m(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 6m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + 6mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln^{2}(x - 1) + 6mx(x - 1)^{e^{x}}*2e^{x}e^{x}ln^{2}(x - 1) + \frac{6mx(x - 1)^{e^{x}}e^{{x}*{2}}*2ln(x - 1)(1 + 0)}{(x - 1)} + 3(\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1) + \frac{3m*2x(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{3mx^{2}(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{2}(x - 1)}{(x - 1)} + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}*2ln(x - 1)(1 + 0)}{(x - 1)(x - 1)} + 6m(x - 1)^{e^{x}}e^{x}ln(x - 1) + 6mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + 6mx(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{6mx(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 12(\frac{-(1 + 0)}{(x - 1)^{2}})mx(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) + \frac{12m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{12mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{12mx(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)} + \frac{12mx(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)(x - 1)} + m*2x(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln^{3}(x - 1) + mx^{2}(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{3}(x - 1) + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}*3ln^{2}(x - 1)(1 + 0)}{(x - 1)} + 3m*2x(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + 3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln^{2}(x - 1) + 3mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}ln^{2}(x - 1) + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}*2ln(x - 1)(1 + 0)}{(x - 1)} + 9(\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) + \frac{9m*2x(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{9mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{9mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)} + \frac{9mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)(x - 1)} - 3(\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) - \frac{3m*2x(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} - \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} - \frac{3mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)^{2}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)^{2}(x - 1)} + 3(\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1) + \frac{3m*2x(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{3mx^{2}(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln(x - 1)}{(x - 1)^{2}} + \frac{3mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}(1 + 0)}{(x - 1)^{2}(x - 1)} + 12(\frac{-(1 + 0)}{(x - 1)^{2}})mx(x - 1)^{e^{x}}e^{x} + \frac{12m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{12mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{12mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 6(\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}} + \frac{6m*2x(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{2}} + m*2x(x - 1)^{e^{x}}e^{x}ln(x - 1) + mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}ln(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{mx^{2}(x - 1)^{e^{x}}e^{x}(1 + 0)}{(x - 1)} + 3(\frac{-(1 + 0)}{(x - 1)^{2}})mx^{2}(x - 1)^{e^{x}}e^{x} + \frac{3m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln^{2}(x - 1) + 9m(x - 1)^{e^{x}}*2e^{x}e^{x}ln^{2}(x - 1) + \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}*2ln(x - 1)(1 + 0)}{(x - 1)} + 9(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1) + \frac{9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{9m(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{2}(x - 1)}{(x - 1)} + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}*2ln(x - 1)(1 + 0)}{(x - 1)(x - 1)} + 27(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) + \frac{27m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{27m(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)} + \frac{27m(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)(x - 1)} + 2(\frac{-3(1 + 0)}{(x - 1)^{4}})mx^{2}(x - 1)^{e^{x}}e^{x} + \frac{2m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} + \frac{2mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{3}} + \frac{2mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - 6(\frac{-2(1 + 0)}{(x - 1)^{3}})mx(x - 1)^{e^{x}}e^{x} - \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{6mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{2}} - \frac{6mx(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - 3(\frac{-3(1 + 0)}{(x - 1)^{4}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}} - \frac{3m*2x(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{3}} - \frac{3mx^{2}(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{3}} - 3(\frac{-2(1 + 0)}{(x - 1)^{3}})mx^{2}(x - 1)^{e^{x}}e^{x} - \frac{3m*2x(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{3mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{2}} - \frac{3mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln^{3}(x - 1) + 3m(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln^{3}(x - 1) + \frac{3m(x - 1)^{e^{x}}e^{{x}*{3}}*3ln^{2}(x - 1)(1 + 0)}{(x - 1)} + 6(\frac{-2(1 + 0)}{(x - 1)^{3}})mx(x - 1)^{e^{x}}e^{{x}*{2}} + \frac{6m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6mx((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{2}} + \frac{6mx(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{2}} + (\frac{-3(1 + 0)}{(x - 1)^{4}})mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}} + \frac{m*2x(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} + \frac{mx^{2}((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}}{(x - 1)^{3}} + \frac{mx^{2}(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}}{(x - 1)^{3}} - 9(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1) - \frac{9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} - \frac{9m(x - 1)^{e^{x}}*2e^{x}e^{x}ln(x - 1)}{(x - 1)^{2}} - \frac{9m(x - 1)^{e^{x}}e^{{x}*{2}}(1 + 0)}{(x - 1)^{2}(x - 1)} + 9(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1) + \frac{9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{9m(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}ln(x - 1)}{(x - 1)^{2}} + \frac{9m(x - 1)^{e^{x}}e^{{x}*{3}}(1 + 0)}{(x - 1)^{2}(x - 1)} + 15(\frac{-(1 + 0)}{(x - 1)^{2}})m(x - 1)^{e^{x}}e^{x} + \frac{15m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)} + \frac{15m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 18(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{{x}*{2}} + \frac{18m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{2}} + \frac{18m(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{2}} + 6(\frac{-3(1 + 0)}{(x - 1)^{4}})m(x - 1)^{e^{x}}e^{x} + \frac{6m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{3}} + \frac{6m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - 9(\frac{-3(1 + 0)}{(x - 1)^{4}})m(x - 1)^{e^{x}}e^{{x}*{2}} - \frac{9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{2}}}{(x - 1)^{3}} - \frac{9m(x - 1)^{e^{x}}*2e^{x}e^{x}}{(x - 1)^{3}} - 9(\frac{-2(1 + 0)}{(x - 1)^{3}})m(x - 1)^{e^{x}}e^{x} - \frac{9m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{x}}{(x - 1)^{2}} - \frac{9m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + 3(\frac{-3(1 + 0)}{(x - 1)^{4}})m(x - 1)^{e^{x}}e^{{x}*{3}} + \frac{3m((x - 1)^{e^{x}}((e^{x})ln(x - 1) + \frac{(e^{x})(1 + 0)}{(x - 1)}))e^{{x}*{3}}}{(x - 1)^{3}} + \frac{3m(x - 1)^{e^{x}}*3e^{{x}*{2}}e^{x}}{(x - 1)^{3}}\\=&33m(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{12m(x - 1)^{e^{x}}e^{{x}*{4}}ln^{3}(x - 1)}{(x - 1)} + 15m(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{108m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + 8mx(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + \frac{4mx^{2}(x - 1)^{e^{x}}e^{{x}*{4}}ln^{3}(x - 1)}{(x - 1)} + 24mx(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{72mx(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} - \frac{6mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)^{2}} + \frac{24mx(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{24mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{30mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + 8mx(x - 1)^{e^{x}}e^{x}ln(x - 1) - \frac{24mx(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{72m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)} + \frac{6mx^{2}(x - 1)^{e^{x}}e^{{x}*{4}}ln^{2}(x - 1)}{(x - 1)^{2}} - \frac{18mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + mx^{2}(x - 1)^{e^{x}}e^{{x}*{4}}ln^{4}(x - 1) + 6mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + 7mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln^{2}(x - 1) + \frac{28mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)} + \frac{24mx(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} + \frac{8mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{3}} - \frac{12mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{3}} + \frac{4mx^{2}(x - 1)^{e^{x}}e^{{x}*{4}}ln(x - 1)}{(x - 1)^{3}} + \frac{24mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} - \frac{24mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} + \frac{24mx(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{48mx(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} + \frac{12mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} + 18m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{3}(x - 1) + mx^{2}(x - 1)^{e^{x}}e^{x}ln(x - 1) + \frac{4mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)} + 3m(x - 1)^{e^{x}}e^{{x}*{4}}ln^{4}(x - 1) - \frac{18m(x - 1)^{e^{x}}e^{{x}*{3}}ln^{2}(x - 1)}{(x - 1)^{2}} + \frac{90m(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{2}} - \frac{54m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{2}} + \frac{18m(x - 1)^{e^{x}}e^{{x}*{4}}ln^{2}(x - 1)}{(x - 1)^{2}} + \frac{24m(x - 1)^{e^{x}}e^{{x}*{2}}ln(x - 1)}{(x - 1)^{3}} - \frac{36m(x - 1)^{e^{x}}e^{{x}*{3}}ln(x - 1)}{(x - 1)^{3}} - \frac{6mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{4}} + \frac{16mx(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} + \frac{11mx^{2}(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{4}} + \frac{8mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} + \frac{12m(x - 1)^{e^{x}}e^{{x}*{4}}ln(x - 1)}{(x - 1)^{3}} - \frac{24mx(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} - \frac{24mx(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{6mx^{2}(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{4}} - \frac{6mx^{2}(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{8mx(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} + \frac{mx^{2}(x - 1)^{e^{x}}e^{{x}*{4}}}{(x - 1)^{4}} + \frac{36m(x - 1)^{e^{x}}e^{x}}{(x - 1)} + \frac{84m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{2}} - \frac{72m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{3}} - \frac{30m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{2}} + \frac{36m(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{3}} - \frac{18m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{4}} + \frac{33m(x - 1)^{e^{x}}e^{{x}*{2}}}{(x - 1)^{4}} + \frac{24m(x - 1)^{e^{x}}e^{x}}{(x - 1)^{3}} - \frac{18m(x - 1)^{e^{x}}e^{{x}*{3}}}{(x - 1)^{4}} + \frac{3m(x - 1)^{e^{x}}e^{{x}*{4}}}{(x - 1)^{4}}\\ \end{split}\end{equation} \]