derivative of-2(arctan(3x-arctan(2x))+x)

解

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

- \frac{2 ( - 6 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ( 4 x ^{2} + 1 )} + 1

解答ステップ

\frac{d}{d x} (- 2 (arctan (3 x) - arctan (2 x)) + x)

和/差の法則を適用:

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

= - \frac{d}{d x} (2 (arctan (3 x) - arctan (2 x))) + \frac{d x}{d x}

\frac{d}{d x} (2 (arctan (3 x) - arctan (2 x))) = \frac{2 ( - 6 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ( 4 x ^{2} + 1 )}

\frac{d x}{d x} = 1

= - \frac{2 ( - 6 x ^{2} + 1 )}{( 9 x ^{2} + 1 ) ( 4 x ^{2} + 1 )} + 1