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

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