There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{ix}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{ix}\right)}{dx}\\=&e^{ix}i\\=&ie^{ix}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( ie^{ix}\right)}{dx}\\=&ie^{ix}i\\=&i^{2}e^{ix}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( i^{2}e^{ix}\right)}{dx}\\=&i^{2}e^{ix}i\\=&i^{3}e^{ix}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( i^{3}e^{ix}\right)}{dx}\\=&i^{3}e^{ix}i\\=&i^{4}e^{ix}\\ \end{split}\end{equation} \]

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