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

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