There are 1 questions in this calculation: for each question, the 4 derivative of R is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {R}^{r}\ with\ respect\ to\ R：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {R}^{r}\right)}{dR}\\=&({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))\\=&\frac{r{R}^{r}}{R}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{r{R}^{r}}{R}\right)}{dR}\\=&\frac{r*-{R}^{r}}{R^{2}} + \frac{r({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R}\\=&\frac{-r{R}^{r}}{R^{2}} + \frac{r^{2}{R}^{r}}{R^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-r{R}^{r}}{R^{2}} + \frac{r^{2}{R}^{r}}{R^{2}}\right)}{dR}\\=&\frac{-r*-2{R}^{r}}{R^{3}} - \frac{r({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R^{2}} + \frac{r^{2}*-2{R}^{r}}{R^{3}} + \frac{r^{2}({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R^{2}}\\=&\frac{2r{R}^{r}}{R^{3}} - \frac{3r^{2}{R}^{r}}{R^{3}} + \frac{r^{3}{R}^{r}}{R^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2r{R}^{r}}{R^{3}} - \frac{3r^{2}{R}^{r}}{R^{3}} + \frac{r^{3}{R}^{r}}{R^{3}}\right)}{dR}\\=&\frac{2r*-3{R}^{r}}{R^{4}} + \frac{2r({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R^{3}} - \frac{3r^{2}*-3{R}^{r}}{R^{4}} - \frac{3r^{2}({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R^{3}} + \frac{r^{3}*-3{R}^{r}}{R^{4}} + \frac{r^{3}({R}^{r}((0)ln(R) + \frac{(r)(1)}{(R)}))}{R^{3}}\\=&\frac{-6r{R}^{r}}{R^{4}} + \frac{11r^{2}{R}^{r}}{R^{4}} - \frac{6r^{3}{R}^{r}}{R^{4}} + \frac{r^{4}{R}^{r}}{R^{4}}\\ \end{split}\end{equation} \]

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