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

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