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.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sh(sh(sh(sh(x))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sh(sh(sh(sh(x))))\right)}{dx}\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)ch(sh(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)ch(sh(x))\right)}{dx}\\=&sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x)))ch(x)ch(sh(x)) + ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch(sh(x)) + ch(sh(sh(sh(x))))ch(sh(sh(x)))sh(x)ch(sh(x)) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)sh(sh(x))ch(x)\\=&sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))\right)}{dx}\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))*2ch(sh(x))sh(sh(x))ch(x)ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))*2ch(x)sh(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))*2ch(sh(x))sh(sh(x))ch(x)ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{2}(sh(x))*2ch(x)sh(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))sh(sh(x))ch(x) + ch(sh(x))ch(x)ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(x))*2ch(x)sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(x))ch^{2}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x)\\=&ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x))\right)}{dx}\\=&sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))*3ch^{2}(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))*3ch^{2}(x)sh(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)*3ch^{2}(sh(x))sh(sh(x))ch(x) + 2ch(sh(x))ch(x)sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))*3ch^{2}(x)sh(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)sh(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))*2ch(sh(x))sh(sh(x))ch(x)ch(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))sh(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))*3ch^{2}(sh(x))sh(sh(x))ch(x)ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)sh(sh(sh(x)))ch(sh(x))ch(x) + 3ch^{2}(sh(x))sh(sh(x))ch(x)ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + ch^{3}(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + ch^{3}(sh(x))ch^{3}(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x)))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + 2ch(sh(x))ch(x)sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))*3ch^{2}(x)sh(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)sh(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(x)ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))*2ch(sh(x))sh(sh(x))ch(x)ch(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))sh(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))*3ch^{2}(sh(x))sh(sh(x))ch(x)ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))*3ch^{2}(x)sh(x) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + ch(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(x)) + ch(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))sh(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)sh(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)ch(x)*2ch(sh(x))sh(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))ch(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))sh(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)*2ch(sh(x))sh(sh(x))ch(x) + ch(sh(x))ch(x)sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + sh(sh(x))sh(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch(sh(sh(x))) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))sh(x)ch(sh(sh(x))) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)sh(sh(sh(x)))ch(sh(x))ch(x) + 3ch^{2}(x)sh(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + ch^{3}(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)ch(sh(x))ch(x)ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))ch(sh(x))ch(x)ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))*3ch^{2}(x)sh(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))sh(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))sh(sh(x))ch(x)\\=&2sh(sh(x))ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x)) + 3sh(sh(sh(x)))ch^{2}(sh(sh(x)))ch(sh(sh(sh(x))))ch^{4}(x)ch^{4}(sh(x)) + 3sh(x)ch^{2}(x)ch^{3}(sh(sh(x)))ch(sh(sh(sh(x))))ch^{3}(sh(x)) + 3sh(sh(x))ch^{3}(sh(sh(x)))ch^{4}(x)ch(sh(sh(sh(x))))ch^{2}(sh(x)) + 2sh(x)ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{2}(x)ch^{3}(sh(x)) + 2sh(sh(sh(x)))ch(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(x)ch^{4}(sh(x)) + 6sh(sh(x))sh(x)sh(sh(sh(sh(x))))ch^{2}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 4sh(sh(sh(sh(x))))sh(x)sh(sh(x))ch^{2}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 4sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(sh(x)))ch^{4}(x)ch^{4}(sh(x))ch(sh(sh(sh(x)))) + 3sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 6sh(sh(sh(sh(x))))sh(sh(sh(x)))sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x))) + 8sh(sh(sh(x)))sh(x)sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x))) + 4sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(x)ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x))) + 5sh(x)ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 4sh(sh(sh(x)))sh(x)sh(sh(x))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 6sh(sh(x))sh(x)sh(sh(sh(x)))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch^{3}(sh(sh(x)))ch^{2}(x)ch^{3}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))ch^{3}(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch^{2}(x)ch(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))ch^{4}(x)ch(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 3sh(sh(sh(sh(x))))sh(x)sh(sh(sh(x)))ch^{2}(x)ch(sh(sh(x)))ch^{3}(sh(x)) + 3sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(x)))ch^{4}(x) + 5sh(x)ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(x)))sh(sh(x))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 3sh(sh(sh(sh(x))))sh(x)sh(sh(x))ch^{2}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{2}(x) + 2sh(sh(sh(sh(x))))ch^{4}(x)ch^{2}(sh(sh(x)))ch^{4}(sh(x)) + 2sh(sh(sh(sh(x))))ch^{2}(x)ch^{2}(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(sh(sh(x)))ch(sh(x))ch^{2}(x) + 2sh(sh(sh(x)))sh(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x)) + 3sh(sh(sh(x)))sh(x)sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(x)) + 2sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x)))ch^{2}(x) + 2sh(sh(sh(x)))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{4}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))ch^{2}(x)ch^{2}(sh(sh(x)))ch^{2}(sh(x)) + sh(sh(sh(x)))sh^{2}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(sh(sh(x))))sh^{2}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(x)ch^{3}(sh(x))ch(sh(sh(x)))ch^{2}(x) + sh(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(sh(x))ch^{4}(x) + 3sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 3sh^{2}(sh(sh(x)))sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x) + sh(sh(sh(sh(x))))sh^{2}(x)ch^{2}(sh(sh(x)))ch^{2}(sh(x)) + 2sh(sh(sh(x)))sh^{2}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + 3sh(sh(sh(x)))ch^{2}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))sh(sh(sh(sh(x))))sh(x)ch(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(x))sh^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(x)))sh(x)sh(sh(x))ch(sh(sh(sh(x))))ch^{2}(x)ch(sh(x)) + sh(sh(sh(sh(x))))ch^{4}(x)ch^{2}(sh(x))ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x)))ch^{4}(x) + sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x))))ch^{4}(x) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + 2sh^{2}(x)sh(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + 2sh(sh(sh(x)))sh(sh(x))sh(x)ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x)ch^{4}(sh(sh(x))) + sh(sh(x))ch^{4}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh^{2}(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh^{2}(sh(x))sh(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(x) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(x))ch(sh(sh(sh(x))))ch^{2}(x)ch(sh(sh(x))) + 2sh^{2}(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x))) + sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{4}(x)ch(sh(sh(x)))ch^{2}(sh(x)) + sh^{2}(sh(x))sh(sh(sh(x)))ch(sh(sh(sh(x))))ch^{4}(x)\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sh(sh(sh(sh(x))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sh(sh(sh(sh(x))))\right)}{dx}\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)ch(sh(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)ch(sh(x))\right)}{dx}\\=&sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x)))ch(x)ch(sh(x)) + ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch(sh(x)) + ch(sh(sh(sh(x))))ch(sh(sh(x)))sh(x)ch(sh(x)) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(x)sh(sh(x))ch(x)\\=&sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))\right)}{dx}\\=&ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))*2ch(sh(x))sh(sh(x))ch(x)ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))*2ch(x)sh(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))*2ch(sh(x))sh(sh(x))ch(x)ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{2}(sh(x))*2ch(x)sh(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))sh(sh(x))ch(x) + ch(sh(x))ch(x)ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(x))*2ch(x)sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(x))ch^{2}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x)\\=&ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x))\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x))\right)}{dx}\\=&sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(sh(x)))ch^{3}(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))*3ch^{2}(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))*3ch^{2}(x)sh(x)ch^{3}(sh(x)) + ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{3}(x)*3ch^{2}(sh(x))sh(sh(x))ch(x) + 2ch(sh(x))ch(x)sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))*3ch^{2}(x)sh(x)ch(sh(x))ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)sh(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))ch^{3}(x)ch(sh(x))*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))*2ch(sh(x))sh(sh(x))ch(x)ch(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))sh(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))*3ch^{2}(sh(x))sh(sh(x))ch(x)ch^{3}(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(x))) + 2sh(sh(sh(x)))sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{3}(x)sh(sh(sh(x)))ch(sh(x))ch(x) + 3ch^{2}(sh(x))sh(sh(x))ch(x)ch^{3}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + ch^{3}(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + ch^{3}(sh(x))ch^{3}(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x)))) + ch^{3}(sh(x))ch^{3}(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + 2ch(sh(x))ch(x)sh(sh(sh(x)))ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))*3ch^{2}(x)sh(x)ch(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)sh(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(sh(x))sh(sh(sh(x)))ch^{3}(x)ch(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(x)ch(sh(sh(x)))ch(sh(x))ch(x)ch^{2}(sh(x))ch(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))*2ch(sh(x))sh(sh(x))ch(x)ch(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))sh(x)ch(sh(sh(sh(x)))) + 2sh(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(sh(x))ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))*3ch^{2}(sh(x))sh(sh(x))ch(x)ch(sh(sh(x)))ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x) + sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))*3ch^{2}(x)sh(x) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + ch(x)sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(x)) + ch(x)ch(sh(sh(x)))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + ch(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))sh(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)sh(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch(x)ch(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)sh(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)ch(x)*2ch(sh(x))sh(sh(x))ch(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))sh(x)ch(x)ch^{2}(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))ch(x)ch^{2}(sh(sh(x)))ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))sh(x)ch^{2}(sh(x)) + sh(sh(sh(sh(x))))sh(x)ch^{2}(sh(sh(x)))ch(x)*2ch(sh(x))sh(sh(x))ch(x) + ch(sh(x))ch(x)sh(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(x)ch(sh(sh(x))) + sh(sh(x))sh(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(x)ch(sh(sh(x))) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))sh(x)ch(sh(sh(x))) + sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(x)sh(sh(sh(x)))ch(sh(x))ch(x) + 3ch^{2}(x)sh(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + ch^{3}(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + ch^{3}(x)ch(sh(x))ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x) + 2ch(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)ch(sh(x))ch(x)ch(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))sh(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(sh(x))) + 2sh(x)sh(sh(x))ch(x)ch(sh(sh(sh(x))))sh(sh(sh(x)))ch(sh(x))ch(x) + ch(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))ch(sh(x))ch(x)ch^{3}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))*3ch^{2}(x)sh(x)ch^{2}(sh(sh(x)))ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)*2ch(sh(sh(x)))sh(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(sh(sh(sh(x))))sh(sh(x))ch^{3}(x)ch^{2}(sh(sh(x)))sh(sh(x))ch(x) + ch(sh(sh(x)))ch(sh(x))ch(x)sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))ch(sh(x))ch(x)ch^{3}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))*3ch^{2}(x)sh(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)sh(sh(sh(sh(x))))ch(sh(sh(x)))ch(sh(x))ch(x)ch(sh(x)) + sh(sh(sh(x)))sh(sh(x))ch^{3}(x)ch(sh(sh(sh(x))))sh(sh(x))ch(x)\\=&2sh(sh(x))ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x)) + 3sh(sh(sh(x)))ch^{2}(sh(sh(x)))ch(sh(sh(sh(x))))ch^{4}(x)ch^{4}(sh(x)) + 3sh(x)ch^{2}(x)ch^{3}(sh(sh(x)))ch(sh(sh(sh(x))))ch^{3}(sh(x)) + 3sh(sh(x))ch^{3}(sh(sh(x)))ch^{4}(x)ch(sh(sh(sh(x))))ch^{2}(sh(x)) + 2sh(x)ch(sh(sh(sh(x))))ch^{3}(sh(sh(x)))ch^{2}(x)ch^{3}(sh(x)) + 2sh(sh(sh(x)))ch(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(x)ch^{4}(sh(x)) + 6sh(sh(x))sh(x)sh(sh(sh(sh(x))))ch^{2}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 4sh(sh(sh(sh(x))))sh(x)sh(sh(x))ch^{2}(x)ch(sh(x))ch^{2}(sh(sh(x))) + 4sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(x))) + sh(sh(sh(x)))ch^{2}(sh(sh(x)))ch^{4}(x)ch^{4}(sh(x))ch(sh(sh(sh(x)))) + 3sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 6sh(sh(sh(sh(x))))sh(sh(sh(x)))sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x))) + 8sh(sh(sh(x)))sh(x)sh(sh(sh(sh(x))))ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x))) + 4sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(x)ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x))) + 5sh(x)ch^{3}(sh(x))ch^{2}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 2sh(sh(x))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(x)))ch(sh(sh(sh(x)))) + 4sh(sh(sh(x)))sh(x)sh(sh(x))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 6sh(sh(x))sh(x)sh(sh(sh(x)))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch^{3}(sh(sh(x)))ch^{2}(x)ch^{3}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))ch^{3}(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch^{2}(x)ch(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))ch^{4}(x)ch(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(x)ch(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 3sh(sh(sh(sh(x))))sh(x)sh(sh(sh(x)))ch^{2}(x)ch(sh(sh(x)))ch^{3}(sh(x)) + 3sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(x))) + 2sh(sh(x))sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(x)))ch^{4}(x) + 5sh(x)ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(x)))sh(sh(x))ch^{2}(x)ch(sh(x))ch(sh(sh(sh(x)))) + 3sh(sh(sh(sh(x))))sh(x)sh(sh(x))ch^{2}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(sh(x)))ch^{3}(sh(x))ch(sh(sh(x)))ch^{2}(x) + 2sh(sh(sh(sh(x))))ch^{4}(x)ch^{2}(sh(sh(x)))ch^{4}(sh(x)) + 2sh(sh(sh(sh(x))))ch^{2}(x)ch^{2}(sh(x))ch^{2}(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(sh(sh(x)))ch(sh(x))ch^{2}(x) + 2sh(sh(sh(x)))sh(sh(x))sh(sh(sh(sh(x))))ch(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x)) + 3sh(sh(sh(x)))sh(x)sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(x)) + 2sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x)))ch^{2}(x) + 2sh(sh(sh(x)))ch^{2}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(x)))ch^{4}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + sh(sh(sh(sh(x))))ch^{2}(x)ch^{2}(sh(sh(x)))ch^{2}(sh(x)) + sh(sh(sh(x)))sh^{2}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + 2sh(sh(sh(sh(x))))sh^{2}(sh(x))ch^{4}(x)ch^{2}(sh(sh(x))) + sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(x)ch^{3}(sh(x))ch(sh(sh(x)))ch^{2}(x) + sh(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(sh(x))ch^{4}(x) + 3sh(sh(x))ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 3sh^{2}(sh(sh(x)))sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x) + sh(sh(sh(sh(x))))sh^{2}(x)ch^{2}(sh(sh(x)))ch^{2}(sh(x)) + 2sh(sh(sh(x)))sh^{2}(sh(x))ch^{4}(x)ch(sh(sh(sh(x)))) + 3sh(sh(sh(x)))ch^{2}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh(sh(x))sh(sh(sh(sh(x))))sh(x)ch(sh(x))ch^{2}(x)ch^{2}(sh(sh(x))) + sh(sh(x))sh^{2}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + sh(sh(sh(x)))sh(x)sh(sh(x))ch(sh(sh(sh(x))))ch^{2}(x)ch(sh(x)) + sh(sh(sh(sh(x))))ch^{4}(x)ch^{2}(sh(x))ch^{2}(sh(sh(x))) + sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x)))ch^{4}(x) + sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x))))ch^{4}(x) + sh(x)ch(sh(sh(x)))ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(x)))ch^{4}(x)ch^{2}(sh(x))ch(sh(sh(sh(x)))) + 2sh^{2}(x)sh(sh(x))ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh(x)sh(sh(sh(sh(x))))sh(sh(x))ch^{2}(x)ch^{2}(sh(sh(x)))ch(sh(x)) + 2sh(sh(sh(x)))sh(sh(x))sh(x)ch^{2}(x)ch(sh(sh(sh(x))))ch(sh(x)) + sh(sh(sh(sh(x))))ch^{4}(sh(x))ch^{4}(x)ch^{4}(sh(sh(x))) + sh(sh(x))ch^{4}(x)ch(sh(sh(sh(x))))ch(sh(sh(x))) + 2sh^{2}(x)sh(sh(sh(x)))ch^{2}(sh(x))ch(sh(sh(sh(x)))) + sh^{2}(sh(x))sh(sh(sh(sh(x))))ch^{2}(sh(sh(x)))ch^{4}(x) + sh(sh(sh(x)))ch^{2}(sh(x))ch^{2}(x)ch(sh(sh(sh(x)))) + sh(sh(x))ch(sh(sh(sh(x))))ch^{2}(x)ch(sh(sh(x))) + 2sh^{2}(x)sh(sh(sh(sh(x))))ch^{2}(sh(x))ch^{2}(sh(sh(x))) + sh(sh(sh(x)))sh(sh(sh(sh(x))))sh(sh(x))ch^{4}(x)ch(sh(sh(x)))ch^{2}(sh(x)) + sh^{2}(sh(x))sh(sh(sh(x)))ch(sh(sh(sh(x))))ch^{4}(x)\\ \end{split}\end{equation} \]