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

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