derivative of (arctan(2x)^2)

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

\int \frac{( x - 1 )}{x ^{2}} d x

\frac{d}{d x} (x^{2} x - 5 x)

a re a y = 2 - e^{x}, y = 10 e^{- x} - 5

d er i v a t i v e f (x) = \frac{ln ( 4 )}{3} e^{x}

d er i v a t i v e y = \frac{5 x - 2}{x}