There are 2 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/2]Find\ the\ first\ derivative\ of\ function\ {cot(\frac{x}{2})}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cot^{2}(\frac{1}{2}x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( cot^{2}(\frac{1}{2}x)\right)}{dx}\\=&-2cot(\frac{1}{2}x)csc^{2}(\frac{1}{2}x)*\frac{1}{2}\\=&-cot(\frac{1}{2}x)csc^{2}(\frac{1}{2}x)\\ \end{split}\end{equation} \]\[ \begin{equation}\begin{split}[2/2]Find\ the\ first\ derivative\ of\ function\ {csc(\frac{x}{2})}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = csc^{2}(\frac{1}{2}x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( csc^{2}(\frac{1}{2}x)\right)}{dx}\\=&-2csc^{2}(\frac{1}{2}x)cot(\frac{1}{2}x)*\frac{1}{2}\\=&-cot(\frac{1}{2}x)csc^{2}(\frac{1}{2}x)\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!