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

\[ \begin{equation}\begin{split}[2/2]Find\ the\ 4th\ derivative\ of\ function\ {ch(x)}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ch^{2}(x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( ch^{2}(x)\right)}{dx}\\=&2ch(x)sh(x)\\=&2sh(x)ch(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2sh(x)ch(x)\right)}{dx}\\=&2ch(x)ch(x) + 2sh(x)sh(x)\\=&2ch^{2}(x) + 2sh^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2ch^{2}(x) + 2sh^{2}(x)\right)}{dx}\\=&2*2ch(x)sh(x) + 2*2sh(x)ch(x)\\=&8sh(x)ch(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 8sh(x)ch(x)\right)}{dx}\\=&8ch(x)ch(x) + 8sh(x)sh(x)\\=&8ch^{2}(x) + 8sh^{2}(x)\\ \end{split}\end{equation} \]





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