There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (6lg(2)x + 8tan(3)x + ln(x)){\frac{1}{cos(x)}}^{sin(x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 6x{\frac{1}{cos(x)}}^{sin(x)}lg(2) + 8x{\frac{1}{cos(x)}}^{sin(x)}tan(3) + {\frac{1}{cos(x)}}^{sin(x)}ln(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 6x{\frac{1}{cos(x)}}^{sin(x)}lg(2) + 8x{\frac{1}{cos(x)}}^{sin(x)}tan(3) + {\frac{1}{cos(x)}}^{sin(x)}ln(x)\right)}{dx}\\=&6{\frac{1}{cos(x)}}^{sin(x)}lg(2) + 6x({\frac{1}{cos(x)}}^{sin(x)}((cos(x))ln(\frac{1}{cos(x)}) + \frac{(sin(x))(\frac{sin(x)}{cos^{2}(x)})}{(\frac{1}{cos(x)})}))lg(2) + \frac{6x{\frac{1}{cos(x)}}^{sin(x)}*0}{ln{10}(2)} + 8{\frac{1}{cos(x)}}^{sin(x)}tan(3) + 8x({\frac{1}{cos(x)}}^{sin(x)}((cos(x))ln(\frac{1}{cos(x)}) + \frac{(sin(x))(\frac{sin(x)}{cos^{2}(x)})}{(\frac{1}{cos(x)})}))tan(3) + 8x{\frac{1}{cos(x)}}^{sin(x)}sec^{2}(3)(0) + ({\frac{1}{cos(x)}}^{sin(x)}((cos(x))ln(\frac{1}{cos(x)}) + \frac{(sin(x))(\frac{sin(x)}{cos^{2}(x)})}{(\frac{1}{cos(x)})}))ln(x) + \frac{{\frac{1}{cos(x)}}^{sin(x)}}{(x)}\\=&6{\frac{1}{cos(x)}}^{sin(x)}lg(2) + 6x{\frac{1}{cos(x)}}^{sin(x)}ln(\frac{1}{cos(x)})lg(2)cos(x) + \frac{6x{\frac{1}{cos(x)}}^{sin(x)}lg(2)sin^{2}(x)}{cos(x)} + 8{\frac{1}{cos(x)}}^{sin(x)}tan(3) + 8x{\frac{1}{cos(x)}}^{sin(x)}ln(\frac{1}{cos(x)})cos(x)tan(3) + \frac{8x{\frac{1}{cos(x)}}^{sin(x)}sin^{2}(x)tan(3)}{cos(x)} + {\frac{1}{cos(x)}}^{sin(x)}ln(\frac{1}{cos(x)})ln(x)cos(x) + \frac{{\frac{1}{cos(x)}}^{sin(x)}ln(x)sin^{2}(x)}{cos(x)} + \frac{{\frac{1}{cos(x)}}^{sin(x)}}{x}\\ \end{split}\end{equation} \]

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