There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sh(x)th(x)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sh(x)th(x)\right)}{dx}\\=&ch(x)th(x) + sh(x)(1 - th^{2}(x))\\=&ch(x)th(x) - sh(x)th^{2}(x) + sh(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ch(x)th(x) - sh(x)th^{2}(x) + sh(x)\right)}{dx}\\=&sh(x)th(x) + ch(x)(1 - th^{2}(x)) - ch(x)th^{2}(x) - sh(x)*2th(x)(1 - th^{2}(x)) + ch(x)\\=&2sh(x)th^{3}(x) - 2ch(x)th^{2}(x) + 2ch(x) - sh(x)th(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2sh(x)th^{3}(x) - 2ch(x)th^{2}(x) + 2ch(x) - sh(x)th(x)\right)}{dx}\\=&2ch(x)th^{3}(x) + 2sh(x)*3th^{2}(x)(1 - th^{2}(x)) - 2sh(x)th^{2}(x) - 2ch(x)*2th(x)(1 - th^{2}(x)) + 2sh(x) - ch(x)th(x) - sh(x)(1 - th^{2}(x))\\=&6ch(x)th^{3}(x) + 5sh(x)th^{2}(x) - 6sh(x)th^{4}(x) - 5ch(x)th(x) + sh(x)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6ch(x)th^{3}(x) + 5sh(x)th^{2}(x) - 6sh(x)th^{4}(x) - 5ch(x)th(x) + sh(x)\right)}{dx}\\=&6sh(x)th^{3}(x) + 6ch(x)*3th^{2}(x)(1 - th^{2}(x)) + 5ch(x)th^{2}(x) + 5sh(x)*2th(x)(1 - th^{2}(x)) - 6ch(x)th^{4}(x) - 6sh(x)*4th^{3}(x)(1 - th^{2}(x)) - 5sh(x)th(x) - 5ch(x)(1 - th^{2}(x)) + ch(x)\\=& - 28sh(x)th^{3}(x) + 28ch(x)th^{2}(x) - 24ch(x)th^{4}(x) + 5sh(x)th(x) + 24sh(x)th^{5}(x) - 4ch(x)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !