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.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{((cf - ah)(\frac{(-cc(gn + jl) - c(bhn + dg + bjm + dl) + bd(h + m))}{(cc(gk + fl) - c(bhk + agm + bfm + ahl) + 2abhm)}) + cj - d)}{(cg - bh)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cj}{(cg - hb)} - \frac{d}{(cg - hb)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cj}{(cg - hb)} - \frac{d}{(cg - hb)}\right)}{dx}\\=&\frac{-(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{3}fgn}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{3}fjl}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fhnb}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fgd}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fjbm}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fld}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cfhbd}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cfbdm}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}ahgn}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}ahjl}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cah^{2}nb}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahgd}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahjbm}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahld}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})ahbdm}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})ah^{2}bd}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + (\frac{-(0 + 0)}{(cg - hb)^{2}})cj + 0 - (\frac{-(0 + 0)}{(cg - hb)^{2}})d + 0\\=&0\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{((cf - ah)(\frac{(-cc(gn + jl) - c(bhn + dg + bjm + dl) + bd(h + m))}{(cc(gk + fl) - c(bhk + agm + bfm + ahl) + 2abhm)}) + cj - d)}{(cg - bh)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cj}{(cg - hb)} - \frac{d}{(cg - hb)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} - \frac{ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)(cg - hb)} + \frac{cj}{(cg - hb)} - \frac{d}{(cg - hb)}\right)}{dx}\\=&\frac{-(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{3}fgn}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{3}fgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{3}fjl}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{3}fjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fhnb}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fhnb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fgd}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fjbm}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}fld}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}fld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cfhbd}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cfhbd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cfbdm}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cfbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}ahgn}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}ahgn}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})c^{2}ahjl}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})c^{2}ahjl}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cah^{2}nb}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cah^{2}nb}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahgd}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahgd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahjbm}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahjbm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})cahld}{(cg - hb)} + \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})cahld}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})ahbdm}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})ahbdm}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 - \frac{(\frac{-(0 + 0 + 0 + 0 + 0 + 0 + 0)}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)^{2}})ah^{2}bd}{(cg - hb)} - \frac{(\frac{-(0 + 0)}{(cg - hb)^{2}})ah^{2}bd}{(c^{2}gk + c^{2}fl - chbk - cagm - cfbm - cahl + 2ahbm)} + 0 + (\frac{-(0 + 0)}{(cg - hb)^{2}})cj + 0 - (\frac{-(0 + 0)}{(cg - hb)^{2}})d + 0\\=&0\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]