derivative y=(arctan(6x))^2

解答

导数

y = (arctan (6 x))^{2}

\frac{12 arctan ( 6 x )}{36 x ^{2} + 1}

求解步骤

\frac{d}{d x} ((arctan (6 x))^{2})

使用连锁律:

2 arctan (6 x) \frac{d}{d x} (arctan (6 x))

= 2 arctan (6 x) \frac{d}{d x} (arctan (6 x))

\frac{d}{d x} (arctan (6 x)) = \frac{6}{36 x ^{2} + 1}

= 2 arctan (6 x) \frac{6}{36 x ^{2} + 1}

化简

2 arctan (6 x) \frac{6}{36 x ^{2} + 1} : \frac{12 arctan ( 6 x )}{36 x ^{2} + 1}

= \frac{12 arctan ( 6 x )}{36 x ^{2} + 1}