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

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