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

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