There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sech(\frac{k(2x - t - i)}{(t - i)})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})\right)}{dx}\\=&-sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})tanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})(2(\frac{-(0 + 0)}{(t - i)^{2}})kx + \frac{2k}{(t - i)} - (\frac{-(0 + 0)}{(t - i)^{2}})kt + 0 - (\frac{-(0 + 0)}{(t - i)^{2}})ki + 0)\\=&\frac{-2ktanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})}{(t - i)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2ktanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})}{(t - i)}\right)}{dx}\\=&-2(\frac{-(0 + 0)}{(t - i)^{2}})ktanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)}) - \frac{2ksech^{2}(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})(2(\frac{-(0 + 0)}{(t - i)^{2}})kx + \frac{2k}{(t - i)} - (\frac{-(0 + 0)}{(t - i)^{2}})kt + 0 - (\frac{-(0 + 0)}{(t - i)^{2}})ki + 0)sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})}{(t - i)} - \frac{2ktanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})*-sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})tanh(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})(2(\frac{-(0 + 0)}{(t - i)^{2}})kx + \frac{2k}{(t - i)} - (\frac{-(0 + 0)}{(t - i)^{2}})kt + 0 - (\frac{-(0 + 0)}{(t - i)^{2}})ki + 0)}{(t - i)}\\=& - \frac{4k^{2}sech^{3}(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})}{(t - i)^{2}} + \frac{4k^{2}tanh^{2}(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})sech(\frac{2kx}{(t - i)} - \frac{kt}{(t - i)} - \frac{ki}{(t - i)})}{(t - i)^{2}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !