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

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