derivative of arctan(x-x^2)

解

\frac{d}{d x} (arctan (x) - x^{2})

\frac{1}{x ^{2} + 1} - 2 x

解答ステップ

\frac{d}{d x} (arctan (x) - x^{2})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (x)) - \frac{d}{d x} (x^{2})

\frac{d}{d x} (arctan (x)) = \frac{1}{x ^{2} + 1}

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1}{x ^{2} + 1} - 2 x