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

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