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

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