There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{{x}^{3}cos(sqrt(7)ln(x))}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{3}cos(ln(x)sqrt(7))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{3}cos(ln(x)sqrt(7))\right)}{dx}\\=&\frac{1}{2}*3x^{2}cos(ln(x)sqrt(7)) + \frac{1}{2}x^{3}*-sin(ln(x)sqrt(7))(\frac{sqrt(7)}{(x)} + ln(x)*0*\frac{1}{2}*7^{\frac{1}{2}})\\=&\frac{3x^{2}cos(ln(x)sqrt(7))}{2} - \frac{x^{2}sin(ln(x)sqrt(7))sqrt(7)}{2}\\ \end{split}\end{equation} \]

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