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

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