There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{60}{(sin(arctan(\frac{(3tan(x))}{({(45 + 36cos(x))}^{\frac{1}{2}})})))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{60}{sin(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{60}{sin(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))}\right)}{dx}\\=&\frac{60*-cos(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))(\frac{(3(\frac{\frac{-1}{2}(36*-sin(x) + 0)}{(36cos(x) + 45)^{\frac{3}{2}}})tan(x) + \frac{3sec^{2}(x)(1)}{(36cos(x) + 45)^{\frac{1}{2}}})}{(1 + (\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}})^{2})})}{sin^{2}(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))}\\=&\frac{-3240sin(x)cos(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))tan(x)}{(36cos(x) + 45)^{\frac{3}{2}}(\frac{9tan^{2}(x)}{(36cos(x) + 45)} + 1)sin^{2}(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))} - \frac{180cos(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))sec^{2}(x)}{(36cos(x) + 45)^{\frac{1}{2}}(\frac{9tan^{2}(x)}{(36cos(x) + 45)} + 1)sin^{2}(arctan(\frac{3tan(x)}{(36cos(x) + 45)^{\frac{1}{2}}}))}\\ \end{split}\end{equation} \]

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