There are 3 questions in this calculation: for each question, the 4 derivative of n is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/3]Find\ the\ 4th\ derivative\ of\ function\ se^{v}e^{n}\ with\ respect\ to\ n：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( se^{v}e^{n}\right)}{dn}\\=&se^{v}*0e^{n} + se^{v}e^{n}\\=&se^{n}e^{v}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( se^{n}e^{v}\right)}{dn}\\=&se^{n}e^{v} + se^{n}e^{v}*0\\=&se^{n}e^{v}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( se^{n}e^{v}\right)}{dn}\\=&se^{n}e^{v} + se^{n}e^{v}*0\\=&se^{n}e^{v}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( se^{n}e^{v}\right)}{dn}\\=&se^{n}e^{v} + se^{n}e^{v}*0\\=&se^{n}e^{v}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}[2/3]Find\ the\ 4th\ derivative\ of\ function\ se^{v}e^{n}te^{e^{n}}\ with\ respect\ to\ n：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ste^{n}e^{v}e^{e^{n}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ste^{n}e^{v}e^{e^{n}}\right)}{dn}\\=&ste^{n}e^{v}e^{e^{n}} + ste^{n}e^{v}*0e^{e^{n}} + ste^{n}e^{v}e^{e^{n}}e^{n}\\=&ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v}\right)}{dn}\\=&ste^{n}e^{v}e^{e^{n}} + ste^{n}e^{v}*0e^{e^{n}} + ste^{n}e^{v}e^{e^{n}}e^{n} + ste^{e^{n}}e^{n}e^{{n}*{2}}e^{v} + ste^{e^{n}}*2e^{n}e^{n}e^{v} + ste^{e^{n}}e^{{n}*{2}}e^{v}*0\\=&ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v} + ste^{{n}*{3}}e^{e^{n}}e^{v} + 2ste^{{n}*{2}}e^{e^{n}}e^{v}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v} + ste^{{n}*{3}}e^{e^{n}}e^{v} + 2ste^{{n}*{2}}e^{e^{n}}e^{v}\right)}{dn}\\=&ste^{n}e^{v}e^{e^{n}} + ste^{n}e^{v}*0e^{e^{n}} + ste^{n}e^{v}e^{e^{n}}e^{n} + ste^{e^{n}}e^{n}e^{{n}*{2}}e^{v} + ste^{e^{n}}*2e^{n}e^{n}e^{v} + ste^{e^{n}}e^{{n}*{2}}e^{v}*0 + st*3e^{{n}*{2}}e^{n}e^{e^{n}}e^{v} + ste^{{n}*{3}}e^{e^{n}}e^{n}e^{v} + ste^{{n}*{3}}e^{e^{n}}e^{v}*0 + 2st*2e^{n}e^{n}e^{e^{n}}e^{v} + 2ste^{{n}*{2}}e^{e^{n}}e^{n}e^{v} + 2ste^{{n}*{2}}e^{e^{n}}e^{v}*0\\=&ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v} + 6ste^{{n}*{3}}e^{e^{n}}e^{v} + 6ste^{{n}*{2}}e^{e^{n}}e^{v} + ste^{{n}*{4}}e^{e^{n}}e^{v}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v} + 6ste^{{n}*{3}}e^{e^{n}}e^{v} + 6ste^{{n}*{2}}e^{e^{n}}e^{v} + ste^{{n}*{4}}e^{e^{n}}e^{v}\right)}{dn}\\=&ste^{n}e^{v}e^{e^{n}} + ste^{n}e^{v}*0e^{e^{n}} + ste^{n}e^{v}e^{e^{n}}e^{n} + ste^{e^{n}}e^{n}e^{{n}*{2}}e^{v} + ste^{e^{n}}*2e^{n}e^{n}e^{v} + ste^{e^{n}}e^{{n}*{2}}e^{v}*0 + 6st*3e^{{n}*{2}}e^{n}e^{e^{n}}e^{v} + 6ste^{{n}*{3}}e^{e^{n}}e^{n}e^{v} + 6ste^{{n}*{3}}e^{e^{n}}e^{v}*0 + 6st*2e^{n}e^{n}e^{e^{n}}e^{v} + 6ste^{{n}*{2}}e^{e^{n}}e^{n}e^{v} + 6ste^{{n}*{2}}e^{e^{n}}e^{v}*0 + st*4e^{{n}*{3}}e^{n}e^{e^{n}}e^{v} + ste^{{n}*{4}}e^{e^{n}}e^{n}e^{v} + ste^{{n}*{4}}e^{e^{n}}e^{v}*0\\=&ste^{n}e^{v}e^{e^{n}} + ste^{e^{n}}e^{{n}*{2}}e^{v} + 25ste^{{n}*{3}}e^{e^{n}}e^{v} + 14ste^{{n}*{2}}e^{e^{n}}e^{v} + 10ste^{{n}*{4}}e^{e^{n}}e^{v} + ste^{{n}*{5}}e^{e^{n}}e^{v}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}[3/3]Find\ the\ 4th\ derivative\ of\ function\ se^{v}e^{n}ty\ with\ respect\ to\ n：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = stye^{v}e^{n}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( stye^{v}e^{n}\right)}{dn}\\=&stye^{v}*0e^{n} + stye^{v}e^{n}\\=&stye^{n}e^{v}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( stye^{n}e^{v}\right)}{dn}\\=&stye^{n}e^{v} + stye^{n}e^{v}*0\\=&stye^{n}e^{v}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( stye^{n}e^{v}\right)}{dn}\\=&stye^{n}e^{v} + stye^{n}e^{v}*0\\=&stye^{n}e^{v}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( stye^{n}e^{v}\right)}{dn}\\=&stye^{n}e^{v} + stye^{n}e^{v}*0\\=&stye^{n}e^{v}\\ \end{split}\end{equation} \]

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