There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt({(tcos(x))}^{2} - {(tsin(x))}^{2})\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(t^{2}cos^{2}(x) - t^{2}sin^{2}(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(t^{2}cos^{2}(x) - t^{2}sin^{2}(x))\right)}{dt}\\=&\frac{(2tcos^{2}(x) + t^{2}*-2cos(x)sin(x)*0 - 2tsin^{2}(x) - t^{2}*2sin(x)cos(x)*0)*\frac{1}{2}}{(t^{2}cos^{2}(x) - t^{2}sin^{2}(x))^{\frac{1}{2}}}\\=&\frac{tcos^{2}(x)}{(t^{2}cos^{2}(x) - t^{2}sin^{2}(x))^{\frac{1}{2}}} - \frac{tsin^{2}(x)}{(t^{2}cos^{2}(x) - t^{2}sin^{2}(x))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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