There are 3 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/3]Find\ the\ first\ derivative\ of\ function\ sin(\frac{1}{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(\frac{1}{x})\right)}{dx}\\=&\frac{cos(\frac{1}{x})*-1}{x^{2}}\\=&\frac{-cos(\frac{1}{x})}{x^{2}}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}[2/3]Find\ the\ first\ derivative\ of\ function\ cos(\frac{1}{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos(\frac{1}{x})\right)}{dx}\\=&\frac{-sin(\frac{1}{x})*-1}{x^{2}}\\=&\frac{sin(\frac{1}{x})}{x^{2}}\\ \end{split}\end{equation} \]

\[ \begin{equation}\begin{split}[3/3]Find\ the\ first\ derivative\ of\ function\ tan(\frac{1}{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan(\frac{1}{x})\right)}{dx}\\=&sec^{2}(\frac{1}{x})(\frac{-1}{x^{2}})\\=&\frac{-sec^{2}(\frac{1}{x})}{x^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！