Find the derivative of f(x)=arctan(2x1−x2)f(x) = \arctan\left(\frac{2x}{1-x^2}\right)f(x)=arctan(1−x22x) and simplify.
21+x2\frac{2}{1+x^2}1+x22
11+x2\frac{1}{1+x^2}1+x21
21−x2\frac{2}{1-x^2}1−x22
sec2(arctan2x1−x2)\sec^2\left(\arctan\frac{2x}{1-x^2}\right)sec2(arctan1−x22x)