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

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