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

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