There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(2{x}^{2} + \frac{x}{7} + 555){\frac{1}{sin(x)}}^{cos(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{1}{sin(x)}}^{cos(x)}ln(2x^{2} + \frac{1}{7}x + 555)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{1}{sin(x)}}^{cos(x)}ln(2x^{2} + \frac{1}{7}x + 555)\right)}{dx}\\=&({\frac{1}{sin(x)}}^{cos(x)}((-sin(x))ln(\frac{1}{sin(x)}) + \frac{(cos(x))(\frac{-cos(x)}{sin^{2}(x)})}{(\frac{1}{sin(x)})}))ln(2x^{2} + \frac{1}{7}x + 555) + \frac{{\frac{1}{sin(x)}}^{cos(x)}(2*2x + \frac{1}{7} + 0)}{(2x^{2} + \frac{1}{7}x + 555)}\\=&-{\frac{1}{sin(x)}}^{cos(x)}ln(\frac{1}{sin(x)})ln(2x^{2} + \frac{1}{7}x + 555)sin(x) - \frac{{\frac{1}{sin(x)}}^{cos(x)}ln(2x^{2} + \frac{1}{7}x + 555)cos^{2}(x)}{sin(x)} + \frac{4x{\frac{1}{sin(x)}}^{cos(x)}}{(2x^{2} + \frac{1}{7}x + 555)} + \frac{{\frac{1}{sin(x)}}^{cos(x)}}{7(2x^{2} + \frac{1}{7}x + 555)}\\ \end{split}\end{equation} \]

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