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

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