There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sin(x){\frac{1}{cos(x)}}^{2} + \frac{(ln(tan(\frac{x}{2} + \frac{pi}{4})))}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{sin(x)}{cos^{2}(x)} + \frac{1}{2}ln(tan(\frac{1}{2}x + \frac{1}{4}pi))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{sin(x)}{cos^{2}(x)} + \frac{1}{2}ln(tan(\frac{1}{2}x + \frac{1}{4}pi))\right)}{dx}\\=&\frac{cos(x)}{cos^{2}(x)} + \frac{sin(x)*2sin(x)}{cos^{3}(x)} + \frac{\frac{1}{2}sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)}{(tan(\frac{1}{2}x + \frac{1}{4}pi))}\\=&\frac{1}{cos(x)} + \frac{2sin^{2}(x)}{cos^{3}(x)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{1}{cos(x)} + \frac{2sin^{2}(x)}{cos^{3}(x)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\right)}{dx}\\=&\frac{sin(x)}{cos^{2}(x)} + \frac{2*2sin(x)cos(x)}{cos^{3}(x)} + \frac{2sin^{2}(x)*3sin(x)}{cos^{4}(x)} + \frac{-sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4tan^{2}(\frac{1}{2}x + \frac{1}{4}pi)} + \frac{2sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)tan(\frac{1}{2}x + \frac{1}{4}pi)(\frac{1}{2} + 0)}{4tan(\frac{1}{2}x + \frac{1}{4}pi)}\\=&\frac{5sin(x)}{cos^{2}(x)} + \frac{6sin^{3}(x)}{cos^{4}(x)} - \frac{sec^{4}(\frac{1}{2}x + \frac{1}{4}pi)}{8tan^{2}(\frac{1}{2}x + \frac{1}{4}pi)} + \frac{sec^{2}(\frac{1}{2}x + \frac{1}{4}pi)}{4}\\ \end{split}\end{equation} \]

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