There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{xarcsin(x)}{(tan({x}^{2}ln(x)))}^{5}{(cos({x}^{3}e^{x}arctan(x)))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))\right)}{dx}\\=&e^{xarcsin(x)}(arcsin(x) + x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))cos^{2}(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x)) + e^{xarcsin(x)}*-2cos(x^{3}e^{x}arctan(x))sin(x^{3}e^{x}arctan(x))(3x^{2}e^{x}arctan(x) + x^{3}e^{x}arctan(x) + x^{3}e^{x}(\frac{(1)}{(1 + (x)^{2})}))tan^{5}(x^{2}ln(x)) + e^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))*5tan^{4}(x^{2}ln(x))sec^{2}(x^{2}ln(x))(2xln(x) + \frac{x^{2}}{(x)})\\=&e^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))arcsin(x)tan^{5}(x^{2}ln(x)) + \frac{xe^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))}{(-x^{2} + 1)^{\frac{1}{2}}} - 6x^{2}e^{xarcsin(x)}e^{x}sin(x^{3}e^{x}arctan(x))cos(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))arctan(x) - 2x^{3}e^{x}e^{xarcsin(x)}sin(x^{3}e^{x}arctan(x))cos(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))arctan(x) - \frac{2x^{3}e^{xarcsin(x)}e^{x}sin(x^{3}e^{x}arctan(x))cos(x^{3}e^{x}arctan(x))tan^{5}(x^{2}ln(x))}{(x^{2} + 1)} + 10xe^{xarcsin(x)}ln(x)cos^{2}(x^{3}e^{x}arctan(x))tan^{4}(x^{2}ln(x))sec^{2}(x^{2}ln(x)) + 5xe^{xarcsin(x)}cos^{2}(x^{3}e^{x}arctan(x))tan^{4}(x^{2}ln(x))sec^{2}(x^{2}ln(x))\\ \end{split}\end{equation} \]

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