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





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