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

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