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

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