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





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