There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {{{tan(x)}^{X}}^{X}}^{X}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{tan(x)}^{X}}^{X}}^{X}\right)}{dx}\\=&({{{tan(x)}^{X}}^{X}}^{X}((0)ln({{tan(x)}^{X}}^{X}) + \frac{(X)(({{tan(x)}^{X}}^{X}((0)ln({tan(x)}^{X}) + \frac{(X)(({tan(x)}^{X}((0)ln(tan(x)) + \frac{(X)(sec^{2}(x)(1))}{(tan(x))})))}{({tan(x)}^{X})})))}{({{tan(x)}^{X}}^{X})}))\\=&\frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{2}(x)}{tan(x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{2}(x)}{tan(x)}\right)}{dx}\\=&\frac{X^{3}({{{tan(x)}^{X}}^{X}}^{X}((0)ln({{tan(x)}^{X}}^{X}) + \frac{(X)(({{tan(x)}^{X}}^{X}((0)ln({tan(x)}^{X}) + \frac{(X)(({tan(x)}^{X}((0)ln(tan(x)) + \frac{(X)(sec^{2}(x)(1))}{(tan(x))})))}{({tan(x)}^{X})})))}{({{tan(x)}^{X}}^{X})}))sec^{2}(x)}{tan(x)} + \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}*-sec^{2}(x)(1)sec^{2}(x)}{tan^{2}(x)} + \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}*2sec^{2}(x)tan(x)}{tan(x)}\\=&\frac{X^{6}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan^{2}(x)} - \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan^{2}(x)} + 2X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{2}(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{X^{6}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan^{2}(x)} - \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan^{2}(x)} + 2X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{2}(x)\right)}{dx}\\=&\frac{X^{6}({{{tan(x)}^{X}}^{X}}^{X}((0)ln({{tan(x)}^{X}}^{X}) + \frac{(X)(({{tan(x)}^{X}}^{X}((0)ln({tan(x)}^{X}) + \frac{(X)(({tan(x)}^{X}((0)ln(tan(x)) + \frac{(X)(sec^{2}(x)(1))}{(tan(x))})))}{({tan(x)}^{X})})))}{({{tan(x)}^{X}}^{X})}))sec^{4}(x)}{tan^{2}(x)} + \frac{X^{6}{{{tan(x)}^{X}}^{X}}^{X}*-2sec^{2}(x)(1)sec^{4}(x)}{tan^{3}(x)} + \frac{X^{6}{{{tan(x)}^{X}}^{X}}^{X}*4sec^{4}(x)tan(x)}{tan^{2}(x)} - \frac{X^{3}({{{tan(x)}^{X}}^{X}}^{X}((0)ln({{tan(x)}^{X}}^{X}) + \frac{(X)(({{tan(x)}^{X}}^{X}((0)ln({tan(x)}^{X}) + \frac{(X)(({tan(x)}^{X}((0)ln(tan(x)) + \frac{(X)(sec^{2}(x)(1))}{(tan(x))})))}{({tan(x)}^{X})})))}{({{tan(x)}^{X}}^{X})}))sec^{4}(x)}{tan^{2}(x)} - \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}*-2sec^{2}(x)(1)sec^{4}(x)}{tan^{3}(x)} - \frac{X^{3}{{{tan(x)}^{X}}^{X}}^{X}*4sec^{4}(x)tan(x)}{tan^{2}(x)} + 2X^{3}({{{tan(x)}^{X}}^{X}}^{X}((0)ln({{tan(x)}^{X}}^{X}) + \frac{(X)(({{tan(x)}^{X}}^{X}((0)ln({tan(x)}^{X}) + \frac{(X)(({tan(x)}^{X}((0)ln(tan(x)) + \frac{(X)(sec^{2}(x)(1))}{(tan(x))})))}{({tan(x)}^{X})})))}{({{tan(x)}^{X}}^{X})}))sec^{2}(x) + 2X^{3}{{{tan(x)}^{X}}^{X}}^{X}*2sec^{2}(x)tan(x)\\=&\frac{X^{9}{{{tan(x)}^{X}}^{X}}^{X}sec^{6}(x)}{tan^{3}(x)} - \frac{3X^{6}{{{tan(x)}^{X}}^{X}}^{X}sec^{6}(x)}{tan^{3}(x)} + \frac{6X^{6}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan(x)} + \frac{2X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{6}(x)}{tan^{3}(x)} - \frac{4X^{3}{{{tan(x)}^{X}}^{X}}^{X}sec^{4}(x)}{tan(x)} + 4X^{3}{{{tan(x)}^{X}}^{X}}^{X}tan(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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