Mathematics
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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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ch(ch(x))\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( ch(ch(x))\right)}{dx}\\=&sh(ch(x))sh(x)\\=&sh(x)sh(ch(x))\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( sh(x)sh(ch(x))\right)}{dx}\\=&ch(x)sh(ch(x)) + sh(x)ch(ch(x))sh(x)\\=&sh(ch(x))ch(x) + sh^{2}(x)ch(ch(x))\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( sh(ch(x))ch(x) + sh^{2}(x)ch(ch(x))\right)}{dx}\\=&ch(ch(x))sh(x)ch(x) + sh(ch(x))sh(x) + 2sh(x)ch(x)ch(ch(x)) + sh^{2}(x)sh(ch(x))sh(x)\\=&sh(x)ch(ch(x))ch(x) + sh(x)sh(ch(x)) + 2sh(x)ch(x)ch(ch(x)) + sh(ch(x))sh^{3}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( sh(x)ch(ch(x))ch(x) + sh(x)sh(ch(x)) + 2sh(x)ch(x)ch(ch(x)) + sh(ch(x))sh^{3}(x)\right)}{dx}\\=&ch(x)ch(ch(x))ch(x) + sh(x)sh(ch(x))sh(x)ch(x) + sh(x)ch(ch(x))sh(x) + ch(x)sh(ch(x)) + sh(x)ch(ch(x))sh(x) + 2ch(x)ch(x)ch(ch(x)) + 2sh(x)sh(x)ch(ch(x)) + 2sh(x)ch(x)sh(ch(x))sh(x) + ch(ch(x))sh(x)sh^{3}(x) + sh(ch(x))*3sh^{2}(x)ch(x)\\=&3ch^{2}(x)ch(ch(x)) + 3sh(ch(x))sh^{2}(x)ch(x) + 4sh^{2}(x)ch(ch(x)) + sh(ch(x))ch(x) + sh^{4}(x)ch(ch(x)) + 3sh^{2}(x)sh(ch(x))ch(x)\\ \end{split}\end{equation} \]





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