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

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