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

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