There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{-135135}{(256{x}^{(\frac{15}{2})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{-135135}{256}}{x^{\frac{15}{2}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{-135135}{256}}{x^{\frac{15}{2}}}\right)}{dx}\\=&\frac{\frac{-135135}{256}*\frac{-15}{2}}{x^{\frac{17}{2}}}\\=&\frac{2027025}{512x^{\frac{17}{2}}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2027025}{512x^{\frac{17}{2}}}\right)}{dx}\\=&\frac{2027025*\frac{-17}{2}}{512x^{\frac{19}{2}}}\\=&\frac{-34459425}{1024x^{\frac{19}{2}}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-34459425}{1024x^{\frac{19}{2}}}\right)}{dx}\\=&\frac{-34459425*\frac{-19}{2}}{1024x^{\frac{21}{2}}}\\=&\frac{654729075}{2048x^{\frac{21}{2}}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{654729075}{2048x^{\frac{21}{2}}}\right)}{dx}\\=&\frac{654729075*\frac{-21}{2}}{2048x^{\frac{23}{2}}}\\=&\frac{-13749310575}{4096x^{\frac{23}{2}}}\\ \end{split}\end{equation} \]

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