There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ ln(sqrt(X + {X}^{X})) + {sqrt(lg(sqrt(X)))}^{X}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(sqrt(X + {X}^{X})) + {sqrt(lg(sqrt(X)))}^{X}\right)}{dx}\\=&\frac{(0 + ({X}^{X}((0)ln(X) + \frac{(X)(0)}{(X)})))*\frac{1}{2}}{(sqrt(X + {X}^{X}))(X + {X}^{X})^{\frac{1}{2}}} + ({sqrt(lg(sqrt(X)))}^{X}((0)ln(sqrt(lg(sqrt(X)))) + \frac{(X)(\frac{0*\frac{1}{2}*\frac{1}{2}}{ln{10}(sqrt(X))(X)^{\frac{1}{2}}(lg(sqrt(X)))^{\frac{1}{2}}})}{(sqrt(lg(sqrt(X))))}))\\=&\frac{0}{4}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{0}{4}\right)}{dx}\\=&0\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 0\right)}{dx}\\=&0\\ \end{split}\end{equation} \]

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