There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -190sin(ln(x)){\frac{1}{x}}^{6} + 90cos(ln(x)){\frac{1}{x}}^{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-190sin(ln(x))}{x^{6}} + \frac{90cos(ln(x))}{x^{6}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-190sin(ln(x))}{x^{6}} + \frac{90cos(ln(x))}{x^{6}}\right)}{dx}\\=&\frac{-190*-6sin(ln(x))}{x^{7}} - \frac{190cos(ln(x))}{x^{6}(x)} + \frac{90*-6cos(ln(x))}{x^{7}} + \frac{90*-sin(ln(x))}{x^{6}(x)}\\=&\frac{1050sin(ln(x))}{x^{7}} - \frac{730cos(ln(x))}{x^{7}}\\ \end{split}\end{equation} \]

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