There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ {sin(x)}^{cos(x)}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( {sin(x)}^{cos(x)}\right)}{dx}\\=&({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))\\=&-{sin(x)}^{cos(x)}ln(sin(x))sin(x) + \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{sin(x)}^{cos(x)}ln(sin(x))sin(x) + \frac{{sin(x)}^{cos(x)}cos^{2}(x)}{sin(x)}\right)}{dx}\\=&-({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))ln(sin(x))sin(x) - \frac{{sin(x)}^{cos(x)}cos(x)sin(x)}{(sin(x))} - {sin(x)}^{cos(x)}ln(sin(x))cos(x) + \frac{({sin(x)}^{cos(x)}((-sin(x))ln(sin(x)) + \frac{(cos(x))(cos(x))}{(sin(x))}))cos^{2}(x)}{sin(x)} + \frac{{sin(x)}^{cos(x)}*-cos(x)cos^{2}(x)}{sin^{2}(x)} + \frac{{sin(x)}^{cos(x)}*-2cos(x)sin(x)}{sin(x)}\\=&{sin(x)}^{cos(x)}ln^{2}(sin(x))sin^{2}(x) - 2{sin(x)}^{cos(x)}ln(sin(x))cos^{2}(x) - 3{sin(x)}^{cos(x)}cos(x) - {sin(x)}^{cos(x)}ln(sin(x))cos(x) + \frac{{sin(x)}^{cos(x)}cos^{4}(x)}{sin^{2}(x)} - \frac{{sin(x)}^{cos(x)}cos^{3}(x)}{sin^{2}(x)}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !