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 o is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{log_{(o + 1)}^{olg(o + 1)}}{o}\ with\ respect\ to\ o：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{log_{o + 1}^{olg(o + 1)}}{o}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{log_{o + 1}^{olg(o + 1)}}{o}\right)}{do}\\=&\frac{-log_{o + 1}^{olg(o + 1)}}{o^{2}} + \frac{(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{o}\\=&\frac{-log_{o + 1}^{olg(o + 1)}}{o^{2}} + \frac{1}{o^{2}ln(o + 1)} + \frac{1}{(o + 1)oln{10}ln(o + 1)lg(o + 1)} - \frac{log_{o + 1}^{olg(o + 1)}}{(o + 1)oln(o + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-log_{o + 1}^{olg(o + 1)}}{o^{2}} + \frac{1}{o^{2}ln(o + 1)} + \frac{1}{(o + 1)oln{10}ln(o + 1)lg(o + 1)} - \frac{log_{o + 1}^{olg(o + 1)}}{(o + 1)oln(o + 1)}\right)}{do}\\=&\frac{--2log_{o + 1}^{olg(o + 1)}}{o^{3}} - \frac{(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{o^{2}} + \frac{-2}{o^{3}ln(o + 1)} + \frac{-(1 + 0)}{o^{2}ln^{2}(o + 1)(o + 1)} + \frac{(\frac{-(1 + 0)}{(o + 1)^{2}})}{oln{10}ln(o + 1)lg(o + 1)} + \frac{-1}{(o + 1)o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{-0}{(o + 1)oln^{2}{10}ln(o + 1)lg(o + 1)} + \frac{-(1 + 0)}{(o + 1)oln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} + \frac{-(1 + 0)}{(o + 1)oln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} - \frac{(\frac{-(1 + 0)}{(o + 1)^{2}})log_{o + 1}^{olg(o + 1)}}{oln(o + 1)} - \frac{-log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{2}ln(o + 1)} - \frac{(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)oln(o + 1)} - \frac{log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)oln^{2}(o + 1)(o + 1)}\\=&\frac{2log_{o + 1}^{olg(o + 1)}}{o^{3}} - \frac{3}{o^{3}ln(o + 1)} - \frac{2}{(o + 1)o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{2}ln(o + 1)} - \frac{1}{(o + 1)^{2}oln{10}ln(o + 1)lg(o + 1)} - \frac{2}{(o + 1)^{2}oln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{1}{(o + 1)^{2}oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{2}{(o + 1)o^{2}ln^{2}(o + 1)} + \frac{log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}oln(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}oln^{2}(o + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2log_{o + 1}^{olg(o + 1)}}{o^{3}} - \frac{3}{o^{3}ln(o + 1)} - \frac{2}{(o + 1)o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{2}ln(o + 1)} - \frac{1}{(o + 1)^{2}oln{10}ln(o + 1)lg(o + 1)} - \frac{2}{(o + 1)^{2}oln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{1}{(o + 1)^{2}oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{2}{(o + 1)o^{2}ln^{2}(o + 1)} + \frac{log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}oln(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}oln^{2}(o + 1)}\right)}{do}\\=&\frac{2*-3log_{o + 1}^{olg(o + 1)}}{o^{4}} + \frac{2(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{o^{3}} - \frac{3*-3}{o^{4}ln(o + 1)} - \frac{3*-(1 + 0)}{o^{3}ln^{2}(o + 1)(o + 1)} - \frac{2(\frac{-(1 + 0)}{(o + 1)^{2}})}{o^{2}ln{10}ln(o + 1)lg(o + 1)} - \frac{2*-2}{(o + 1)o^{3}ln{10}ln(o + 1)lg(o + 1)} - \frac{2*-0}{(o + 1)o^{2}ln^{2}{10}ln(o + 1)lg(o + 1)} - \frac{2*-(1 + 0)}{(o + 1)o^{2}ln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} - \frac{2*-(1 + 0)}{(o + 1)o^{2}ln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} + \frac{2(\frac{-(1 + 0)}{(o + 1)^{2}})log_{o + 1}^{olg(o + 1)}}{o^{2}ln(o + 1)} + \frac{2*-2log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{3}ln(o + 1)} + \frac{2(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)o^{2}ln(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)o^{2}ln^{2}(o + 1)(o + 1)} - \frac{(\frac{-2(1 + 0)}{(o + 1)^{3}})}{oln{10}ln(o + 1)lg(o + 1)} - \frac{-1}{(o + 1)^{2}o^{2}ln{10}ln(o + 1)lg(o + 1)} - \frac{-0}{(o + 1)^{2}oln^{2}{10}ln(o + 1)lg(o + 1)} - \frac{-(1 + 0)}{(o + 1)^{2}oln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} - \frac{-(1 + 0)}{(o + 1)^{2}oln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} - \frac{2(\frac{-2(1 + 0)}{(o + 1)^{3}})}{oln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{2*-1}{(o + 1)^{2}o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{2*-0}{(o + 1)^{2}oln^{2}{10}ln^{2}(o + 1)lg(o + 1)} - \frac{2*-2(1 + 0)}{(o + 1)^{2}oln{10}ln^{3}(o + 1)(o + 1)lg(o + 1)} - \frac{2*-(1 + 0)}{(o + 1)^{2}oln{10}ln^{2}(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} - \frac{(\frac{-2(1 + 0)}{(o + 1)^{3}})}{oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{-1}{(o + 1)^{2}o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{-2*0}{(o + 1)^{2}oln^{3}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{-(1 + 0)}{(o + 1)^{2}oln^{2}{10}ln^{2}(o + 1)(o + 1)lg^{2}(o + 1)} - \frac{-2(1 + 0)}{(o + 1)^{2}oln^{2}{10}ln(o + 1)lg^{3}(o + 1)ln{10}(o + 1)} - \frac{2(\frac{-(1 + 0)}{(o + 1)^{2}})}{o^{2}ln^{2}(o + 1)} - \frac{2*-2}{(o + 1)o^{3}ln^{2}(o + 1)} - \frac{2*-2(1 + 0)}{(o + 1)o^{2}ln^{3}(o + 1)(o + 1)} + \frac{(\frac{-2(1 + 0)}{(o + 1)^{3}})log_{o + 1}^{olg(o + 1)}}{oln(o + 1)} + \frac{-log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln(o + 1)} + \frac{(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{2}oln(o + 1)} + \frac{log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)^{2}oln^{2}(o + 1)(o + 1)} + \frac{2(\frac{-2(1 + 0)}{(o + 1)^{3}})log_{o + 1}^{olg(o + 1)}}{oln^{2}(o + 1)} + \frac{2*-log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} + \frac{2(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{2}oln^{2}(o + 1)} + \frac{2log_{o + 1}^{olg(o + 1)}*-2(1 + 0)}{(o + 1)^{2}oln^{3}(o + 1)(o + 1)}\\=&\frac{-6log_{o + 1}^{olg(o + 1)}}{o^{4}} + \frac{11}{o^{4}ln(o + 1)} + \frac{6}{(o + 1)o^{3}ln{10}ln(o + 1)lg(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{3}ln(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{6}{(o + 1)^{2}o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{3log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln(o + 1)} + \frac{2}{(o + 1)^{3}oln{10}ln(o + 1)lg(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} + \frac{6}{(o + 1)^{3}oln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{3}oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{6}{(o + 1)^{3}oln{10}ln^{3}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{3}oln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} + \frac{2}{(o + 1)^{3}oln^{3}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{9}{(o + 1)o^{3}ln^{2}(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} + \frac{6}{(o + 1)^{2}o^{2}ln^{3}(o + 1)} - \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln^{2}(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln^{3}(o + 1)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6log_{o + 1}^{olg(o + 1)}}{o^{4}} + \frac{11}{o^{4}ln(o + 1)} + \frac{6}{(o + 1)o^{3}ln{10}ln(o + 1)lg(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{3}ln(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{6}{(o + 1)^{2}o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{3log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln(o + 1)} + \frac{2}{(o + 1)^{3}oln{10}ln(o + 1)lg(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} + \frac{6}{(o + 1)^{3}oln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{3}oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{6}{(o + 1)^{3}oln{10}ln^{3}(o + 1)lg(o + 1)} + \frac{3}{(o + 1)^{3}oln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} + \frac{2}{(o + 1)^{3}oln^{3}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{9}{(o + 1)o^{3}ln^{2}(o + 1)} + \frac{3}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} + \frac{6}{(o + 1)^{2}o^{2}ln^{3}(o + 1)} - \frac{2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln^{2}(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}oln^{3}(o + 1)}\right)}{do}\\=&\frac{-6*-4log_{o + 1}^{olg(o + 1)}}{o^{5}} - \frac{6(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{o^{4}} + \frac{11*-4}{o^{5}ln(o + 1)} + \frac{11*-(1 + 0)}{o^{4}ln^{2}(o + 1)(o + 1)} + \frac{6(\frac{-(1 + 0)}{(o + 1)^{2}})}{o^{3}ln{10}ln(o + 1)lg(o + 1)} + \frac{6*-3}{(o + 1)o^{4}ln{10}ln(o + 1)lg(o + 1)} + \frac{6*-0}{(o + 1)o^{3}ln^{2}{10}ln(o + 1)lg(o + 1)} + \frac{6*-(1 + 0)}{(o + 1)o^{3}ln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} + \frac{6*-(1 + 0)}{(o + 1)o^{3}ln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} - \frac{6(\frac{-(1 + 0)}{(o + 1)^{2}})log_{o + 1}^{olg(o + 1)}}{o^{3}ln(o + 1)} - \frac{6*-3log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{4}ln(o + 1)} - \frac{6(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)o^{3}ln(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)o^{3}ln^{2}(o + 1)(o + 1)} + \frac{3(\frac{-2(1 + 0)}{(o + 1)^{3}})}{o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{3*-2}{(o + 1)^{2}o^{3}ln{10}ln(o + 1)lg(o + 1)} + \frac{3*-0}{(o + 1)^{2}o^{2}ln^{2}{10}ln(o + 1)lg(o + 1)} + \frac{3*-(1 + 0)}{(o + 1)^{2}o^{2}ln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} + \frac{3*-(1 + 0)}{(o + 1)^{2}o^{2}ln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} + \frac{6(\frac{-2(1 + 0)}{(o + 1)^{3}})}{o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-2}{(o + 1)^{2}o^{3}ln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-0}{(o + 1)^{2}o^{2}ln^{2}{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-2(1 + 0)}{(o + 1)^{2}o^{2}ln{10}ln^{3}(o + 1)(o + 1)lg(o + 1)} + \frac{6*-(1 + 0)}{(o + 1)^{2}o^{2}ln{10}ln^{2}(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} + \frac{3(\frac{-2(1 + 0)}{(o + 1)^{3}})}{o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-2}{(o + 1)^{2}o^{3}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-2*0}{(o + 1)^{2}o^{2}ln^{3}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-(1 + 0)}{(o + 1)^{2}o^{2}ln^{2}{10}ln^{2}(o + 1)(o + 1)lg^{2}(o + 1)} + \frac{3*-2(1 + 0)}{(o + 1)^{2}o^{2}ln^{2}{10}ln(o + 1)lg^{3}(o + 1)ln{10}(o + 1)} - \frac{3(\frac{-2(1 + 0)}{(o + 1)^{3}})log_{o + 1}^{olg(o + 1)}}{o^{2}ln(o + 1)} - \frac{3*-2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{3}ln(o + 1)} - \frac{3(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{2}o^{2}ln(o + 1)} - \frac{3log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)^{2}o^{2}ln^{2}(o + 1)(o + 1)} + \frac{2(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln{10}ln(o + 1)lg(o + 1)} + \frac{2*-1}{(o + 1)^{3}o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{2*-0}{(o + 1)^{3}oln^{2}{10}ln(o + 1)lg(o + 1)} + \frac{2*-(1 + 0)}{(o + 1)^{3}oln{10}ln^{2}(o + 1)(o + 1)lg(o + 1)} + \frac{2*-(1 + 0)}{(o + 1)^{3}oln{10}ln(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} - \frac{6(\frac{-2(1 + 0)}{(o + 1)^{3}})log_{o + 1}^{olg(o + 1)}}{o^{2}ln^{2}(o + 1)} - \frac{6*-2log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{3}ln^{2}(o + 1)} - \frac{6(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{2}o^{2}ln^{2}(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}*-2(1 + 0)}{(o + 1)^{2}o^{2}ln^{3}(o + 1)(o + 1)} + \frac{6(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-1}{(o + 1)^{3}o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-0}{(o + 1)^{3}oln^{2}{10}ln^{2}(o + 1)lg(o + 1)} + \frac{6*-2(1 + 0)}{(o + 1)^{3}oln{10}ln^{3}(o + 1)(o + 1)lg(o + 1)} + \frac{6*-(1 + 0)}{(o + 1)^{3}oln{10}ln^{2}(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} + \frac{3(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-1}{(o + 1)^{3}o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-2*0}{(o + 1)^{3}oln^{3}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{3*-(1 + 0)}{(o + 1)^{3}oln^{2}{10}ln^{2}(o + 1)(o + 1)lg^{2}(o + 1)} + \frac{3*-2(1 + 0)}{(o + 1)^{3}oln^{2}{10}ln(o + 1)lg^{3}(o + 1)ln{10}(o + 1)} + \frac{6(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln{10}ln^{3}(o + 1)lg(o + 1)} + \frac{6*-1}{(o + 1)^{3}o^{2}ln{10}ln^{3}(o + 1)lg(o + 1)} + \frac{6*-0}{(o + 1)^{3}oln^{2}{10}ln^{3}(o + 1)lg(o + 1)} + \frac{6*-3(1 + 0)}{(o + 1)^{3}oln{10}ln^{4}(o + 1)(o + 1)lg(o + 1)} + \frac{6*-(1 + 0)}{(o + 1)^{3}oln{10}ln^{3}(o + 1)lg^{2}(o + 1)ln{10}(o + 1)} + \frac{3(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} + \frac{3*-1}{(o + 1)^{3}o^{2}ln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} + \frac{3*-2*0}{(o + 1)^{3}oln^{3}{10}ln^{2}(o + 1)lg^{2}(o + 1)} + \frac{3*-2(1 + 0)}{(o + 1)^{3}oln^{2}{10}ln^{3}(o + 1)(o + 1)lg^{2}(o + 1)} + \frac{3*-2(1 + 0)}{(o + 1)^{3}oln^{2}{10}ln^{2}(o + 1)lg^{3}(o + 1)ln{10}(o + 1)} + \frac{2(\frac{-3(1 + 0)}{(o + 1)^{4}})}{oln^{3}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{2*-1}{(o + 1)^{3}o^{2}ln^{3}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{2*-3*0}{(o + 1)^{3}oln^{4}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{2*-(1 + 0)}{(o + 1)^{3}oln^{3}{10}ln^{2}(o + 1)(o + 1)lg^{3}(o + 1)} + \frac{2*-3(1 + 0)}{(o + 1)^{3}oln^{3}{10}ln(o + 1)lg^{4}(o + 1)ln{10}(o + 1)} + \frac{9(\frac{-(1 + 0)}{(o + 1)^{2}})}{o^{3}ln^{2}(o + 1)} + \frac{9*-3}{(o + 1)o^{4}ln^{2}(o + 1)} + \frac{9*-2(1 + 0)}{(o + 1)o^{3}ln^{3}(o + 1)(o + 1)} + \frac{3(\frac{-2(1 + 0)}{(o + 1)^{3}})}{o^{2}ln^{2}(o + 1)} + \frac{3*-2}{(o + 1)^{2}o^{3}ln^{2}(o + 1)} + \frac{3*-2(1 + 0)}{(o + 1)^{2}o^{2}ln^{3}(o + 1)(o + 1)} + \frac{6(\frac{-2(1 + 0)}{(o + 1)^{3}})}{o^{2}ln^{3}(o + 1)} + \frac{6*-2}{(o + 1)^{2}o^{3}ln^{3}(o + 1)} + \frac{6*-3(1 + 0)}{(o + 1)^{2}o^{2}ln^{4}(o + 1)(o + 1)} - \frac{2(\frac{-3(1 + 0)}{(o + 1)^{4}})log_{o + 1}^{olg(o + 1)}}{oln(o + 1)} - \frac{2*-log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln(o + 1)} - \frac{2(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{3}oln(o + 1)} - \frac{2log_{o + 1}^{olg(o + 1)}*-(1 + 0)}{(o + 1)^{3}oln^{2}(o + 1)(o + 1)} - \frac{6(\frac{-3(1 + 0)}{(o + 1)^{4}})log_{o + 1}^{olg(o + 1)}}{oln^{2}(o + 1)} - \frac{6*-log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln^{2}(o + 1)} - \frac{6(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{3}oln^{2}(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}*-2(1 + 0)}{(o + 1)^{3}oln^{3}(o + 1)(o + 1)} - \frac{6(\frac{-3(1 + 0)}{(o + 1)^{4}})log_{o + 1}^{olg(o + 1)}}{oln^{3}(o + 1)} - \frac{6*-log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln^{3}(o + 1)} - \frac{6(\frac{(\frac{(lg(o + 1) + \frac{o(1 + 0)}{ln{10}(o + 1)})}{(olg(o + 1))} - \frac{(1 + 0)log_{o + 1}^{olg(o + 1)}}{(o + 1)})}{(ln(o + 1))})}{(o + 1)^{3}oln^{3}(o + 1)} - \frac{6log_{o + 1}^{olg(o + 1)}*-3(1 + 0)}{(o + 1)^{3}oln^{4}(o + 1)(o + 1)}\\=&\frac{24log_{o + 1}^{olg(o + 1)}}{o^{5}} - \frac{50}{o^{5}ln(o + 1)} - \frac{24}{(o + 1)o^{4}ln{10}ln(o + 1)lg(o + 1)} + \frac{24log_{o + 1}^{olg(o + 1)}}{(o + 1)o^{4}ln(o + 1)} - \frac{12}{(o + 1)^{2}o^{3}ln{10}ln(o + 1)lg(o + 1)} - \frac{24}{(o + 1)^{2}o^{3}ln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{12}{(o + 1)^{2}o^{3}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} + \frac{12log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{3}ln(o + 1)} - \frac{8}{(o + 1)^{3}o^{2}ln{10}ln(o + 1)lg(o + 1)} + \frac{24log_{o + 1}^{olg(o + 1)}}{(o + 1)^{2}o^{3}ln^{2}(o + 1)} - \frac{24}{(o + 1)^{3}o^{2}ln{10}ln^{2}(o + 1)lg(o + 1)} - \frac{12}{(o + 1)^{3}o^{2}ln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{24}{(o + 1)^{3}o^{2}ln{10}ln^{3}(o + 1)lg(o + 1)} - \frac{12}{(o + 1)^{3}o^{2}ln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} - \frac{8}{(o + 1)^{3}o^{2}ln^{3}{10}ln(o + 1)lg^{3}(o + 1)} - \frac{6}{(o + 1)^{4}oln{10}ln(o + 1)lg(o + 1)} + \frac{8log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln(o + 1)} - \frac{22}{(o + 1)^{4}oln{10}ln^{2}(o + 1)lg(o + 1)} + \frac{24log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln^{2}(o + 1)} - \frac{11}{(o + 1)^{4}oln^{2}{10}ln(o + 1)lg^{2}(o + 1)} - \frac{36}{(o + 1)^{4}oln{10}ln^{3}(o + 1)lg(o + 1)} - \frac{18}{(o + 1)^{4}oln^{2}{10}ln^{2}(o + 1)lg^{2}(o + 1)} - \frac{12}{(o + 1)^{4}oln^{3}{10}ln(o + 1)lg^{3}(o + 1)} + \frac{24log_{o + 1}^{olg(o + 1)}}{(o + 1)^{3}o^{2}ln^{3}(o + 1)} - \frac{24}{(o + 1)^{4}oln{10}ln^{4}(o + 1)lg(o + 1)} - \frac{12}{(o + 1)^{4}oln^{2}{10}ln^{3}(o + 1)lg^{2}(o + 1)} - \frac{8}{(o + 1)^{4}oln^{3}{10}ln^{2}(o + 1)lg^{3}(o + 1)} - \frac{6}{(o + 1)^{4}oln^{4}{10}ln(o + 1)lg^{4}(o + 1)} - \frac{44}{(o + 1)o^{4}ln^{2}(o + 1)} - \frac{36}{(o + 1)^{2}o^{3}ln^{3}(o + 1)} - \frac{18}{(o + 1)^{2}o^{3}ln^{2}(o + 1)} - \frac{8}{(o + 1)^{3}o^{2}ln^{2}(o + 1)} - \frac{24}{(o + 1)^{3}o^{2}ln^{3}(o + 1)} - \frac{24}{(o + 1)^{3}o^{2}ln^{4}(o + 1)} + \frac{6log_{o + 1}^{olg(o + 1)}}{(o + 1)^{4}oln(o + 1)} + \frac{22log_{o + 1}^{olg(o + 1)}}{(o + 1)^{4}oln^{2}(o + 1)} + \frac{36log_{o + 1}^{olg(o + 1)}}{(o + 1)^{4}oln^{3}(o + 1)} + \frac{24log_{o + 1}^{olg(o + 1)}}{(o + 1)^{4}oln^{4}(o + 1)}\\ \end{split}\end{equation} \]