derivative y=(arctan(4x))^2

解答

导数

y = (arctan (4 x))^{2}

\frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

求解步骤

\frac{d}{d x} ((arctan (4 x))^{2})

使用连锁律:

2 arctan (4 x) \frac{d}{d x} (arctan (4 x))

= 2 arctan (4 x) \frac{d}{d x} (arctan (4 x))

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= 2 arctan (4 x) \frac{4}{16 x ^{2} + 1}

化简

2 arctan (4 x) \frac{4}{16 x ^{2} + 1} : \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

= \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

\int \frac{x - 2}{x ^{2}} d x

\frac{d}{d x} (x e^{x y})

\frac{d}{d x} (8 x^{- 3})

d er i v a t i v e \frac{x}{11} - \frac{11}{x}

\int_{0}^{2 \cdot π} sin (t) d t