There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ sin((\frac{pi}{2})x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sin(\frac{1}{2}pix)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(\frac{1}{2}pix)\right)}{dx}\\=&cos(\frac{1}{2}pix)*\frac{1}{2}pi\\=&\frac{picos(\frac{1}{2}pix)}{2}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{picos(\frac{1}{2}pix)}{2}\right)}{dx}\\=&\frac{pi*-sin(\frac{1}{2}pix)*\frac{1}{2}pi}{2}\\=&\frac{-p^{2}i^{2}sin(\frac{1}{2}pix)}{4}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-p^{2}i^{2}sin(\frac{1}{2}pix)}{4}\right)}{dx}\\=&\frac{-p^{2}i^{2}cos(\frac{1}{2}pix)*\frac{1}{2}pi}{4}\\=&\frac{-p^{3}i^{3}cos(\frac{1}{2}pix)}{8}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-p^{3}i^{3}cos(\frac{1}{2}pix)}{8}\right)}{dx}\\=&\frac{-p^{3}i^{3}*-sin(\frac{1}{2}pix)*\frac{1}{2}pi}{8}\\=&\frac{p^{4}i^{4}sin(\frac{1}{2}pix)}{16}\\ \end{split}\end{equation} \]

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