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

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