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

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