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

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