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

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