There are 1 questions in this calculation: for each question, the 4 derivative of sin is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ({sin(x)}^{cos(x)})\ with\ respect\ to\ sin：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {sin(x)}^{cos(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {sin(x)}^{cos(x)}\right)}{dsin}\\=&({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))\\=&\frac{{sin(x)}^{cos(x)}cos(x)}{sin(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{sin(x)}^{cos(x)}cos(x)}{sin(x)}\right)}{dsin}\\=&\frac{-{sin(x)}^{cos(x)}cos(x)}{sin^{2}} + \frac{({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}*-sin(x)*0}{sin(x)}\\=&\frac{-{sin(x)}^{cos(x)}cos(x)}{sin^{2}} + \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{sin(x)}^{cos(x)}cos(x)}{sin^{2}} + \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)^{2}}\right)}{dsin}\\=&\frac{--2{sin(x)}^{cos(x)}cos(x)}{sin^{3}} - \frac{({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos(x)}{sin^{2}} - \frac{{sin(x)}^{cos(x)}*-sin(x)*0}{sin^{2}} + \frac{-2{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{3}} + \frac{({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos^{2}(x)}{sin(x)^{2}} + \frac{{sin(x)}^{cos(x)}*-2cos(x)sin(x)*0}{sin(x)^{2}}\\=&\frac{2{sin(x)}^{cos(x)}cos(x)}{sin^{3}} - \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)sin^{2}} - \frac{2{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{3}} + \frac{{sin(x)}^{cos(x)}cos^{3}(x)}{sin(x)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2{sin(x)}^{cos(x)}cos(x)}{sin^{3}} - \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)sin^{2}} - \frac{2{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{3}} + \frac{{sin(x)}^{cos(x)}cos^{3}(x)}{sin(x)^{3}}\right)}{dsin}\\=&\frac{2*-3{sin(x)}^{cos(x)}cos(x)}{sin^{4}} + \frac{2({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos(x)}{sin^{3}} + \frac{2{sin(x)}^{cos(x)}*-sin(x)*0}{sin^{3}} - \frac{-{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{2}sin^{2}} - \frac{-2{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)sin^{3}} - \frac{({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos^{2}(x)}{sin(x)sin^{2}} - \frac{{sin(x)}^{cos(x)}*-2cos(x)sin(x)*0}{sin(x)sin^{2}} - \frac{2*-3{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{4}} - \frac{2({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos^{2}(x)}{sin^{3}} - \frac{2{sin(x)}^{cos(x)}*-2cos(x)sin(x)*0}{sin^{3}} + \frac{-3{sin(x)}^{cos(x)}cos^{3}(x)}{sin^{4}} + \frac{({sin(x)}^{cos(x)}((-sin(x)*0)ln(sin(x)) + \frac{(cos(x))(1)}{(sin(x))}))cos^{3}(x)}{sin(x)^{3}} + \frac{{sin(x)}^{cos(x)}*-3cos^{2}(x)sin(x)*0}{sin(x)^{3}}\\=&\frac{-6{sin(x)}^{cos(x)}cos(x)}{sin^{4}} + \frac{4{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)sin^{3}} + \frac{7{sin(x)}^{cos(x)}cos^{2}(x)}{sin^{4}} - \frac{{sin(x)}^{cos(x)}cos^{3}(x)}{sin(x)^{2}sin^{2}} - \frac{2{sin(x)}^{cos(x)}cos^{3}(x)}{sin(x)sin^{3}} - \frac{3{sin(x)}^{cos(x)}cos^{3}(x)}{sin^{4}} + \frac{{sin(x)}^{cos(x)}cos^{4}(x)}{sin(x)^{4}}\\ \end{split}\end{equation} \]

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