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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sh(x)ch(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sh(x)ch(x)\right)}{dx}\\=&ch(x)ch(x) + sh(x)sh(x)\\=&ch^{2}(x) + sh^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ch^{2}(x) + sh^{2}(x)\right)}{dx}\\=&2ch(x)sh(x) + 2sh(x)ch(x)\\=&4sh(x)ch(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 4sh(x)ch(x)\right)}{dx}\\=&4ch(x)ch(x) + 4sh(x)sh(x)\\=&4ch^{2}(x) + 4sh^{2}(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 4ch^{2}(x) + 4sh^{2}(x)\right)}{dx}\\=&4*2ch(x)sh(x) + 4*2sh(x)ch(x)\\=&16sh(x)ch(x)\\ \end{split}\end{equation} \]





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