There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ arcsin((\frac{1}{3})(13 - 12sin(arccos(\frac{5cos(x)}{sqrt(169 + 120sin(x))}))))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arcsin(-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arcsin(-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})\right)}{dx}\\=&(\frac{(-4cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))(\frac{-(\frac{5*-sin(x)}{sqrt(120sin(x) + 169)} + \frac{5cos(x)*-(120cos(x) + 0)*\frac{1}{2}}{(120sin(x) + 169)(120sin(x) + 169)^{\frac{1}{2}}})}{((1 - (\frac{5cos(x)}{sqrt(120sin(x) + 169)})^{2})^{\frac{1}{2}})}) + 0)}{((1 - (-4sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{13}{3})^{2})^{\frac{1}{2}})})\\=&\frac{-20sin(x)cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))}{(-16sin^{2}(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{104}{3}sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) - \frac{160}{9})^{\frac{1}{2}}(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}sqrt(120sin(x) + 169)} - \frac{1200cos^{2}(x)cos(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)}))}{(-16sin^{2}(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) + \frac{104}{3}sin(arccos(\frac{5cos(x)}{sqrt(120sin(x) + 169)})) - \frac{160}{9})^{\frac{1}{2}}(\frac{-25cos^{2}(x)}{sqrt(120sin(x) + 169)^{2}} + 1)^{\frac{1}{2}}(120sin(x) + 169)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！