There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (ln(5))({5}^{sin(x)})(cos(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {5}^{sin(x)}ln(5)cos(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {5}^{sin(x)}ln(5)cos(x)\right)}{dx}\\=&({5}^{sin(x)}((cos(x))ln(5) + \frac{(sin(x))(0)}{(5)}))ln(5)cos(x) + \frac{{5}^{sin(x)}*0cos(x)}{(5)} + {5}^{sin(x)}ln(5)*-sin(x)\\=&{5}^{sin(x)}ln^{2}(5)cos^{2}(x) - {5}^{sin(x)}ln(5)sin(x)\\ \end{split}\end{equation} \]

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