There are 1 questions in this calculation: for each question, the 1 derivative of t is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(tan(\frac{t}{2}))\ with\ respect\ to\ t：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(tan(\frac{1}{2}t))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(tan(\frac{1}{2}t))\right)}{dt}\\=&\frac{sec^{2}(\frac{1}{2}t)(\frac{1}{2})}{ln{10}(tan(\frac{1}{2}t))}\\=&\frac{sec^{2}(\frac{1}{2}t)}{2ln{10}tan(\frac{1}{2}t)}\\ \end{split}\end{equation} \]

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