There are 1 questions in this calculation: for each question, the 1 derivative of y is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 4yarctan(2y) - \frac{ln(4{y}^{2} + 1)}{2}\ with\ respect\ to\ y：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4yarctan(2y) - \frac{1}{2}ln(4y^{2} + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4yarctan(2y) - \frac{1}{2}ln(4y^{2} + 1)\right)}{dy}\\=&4arctan(2y) + 4y(\frac{(2)}{(1 + (2y)^{2})}) - \frac{\frac{1}{2}(4*2y + 0)}{(4y^{2} + 1)}\\=&4arctan(2y) + \frac{8y}{(4y^{2} + 1)} - \frac{4y}{(4y^{2} + 1)}\\ \end{split}\end{equation} \]

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