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人気のある微分積分 >

derivative (arctan(3x))^2

解

導関数

(arctan (3 x))^{2}

解

\frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

解答ステップ

\frac{d}{d x} ((arctan (3 x))^{2})

連鎖法則を適用:

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

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

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

= 2 arctan (3 x) \frac{3}{9 x ^{2} + 1}

簡素化

2 arctan (3 x) \frac{3}{9 x ^{2} + 1} : \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

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

グラフ

人気の例

derivative of 15sin(-pixtan(2/3 pix))

\frac{d}{d x} (15 sin (- π x) tan (\frac{2}{3} π x))

integral of (2-v)/(v^2+2v-3)

\int \frac{2 - v}{v ^{2} + 2 v - 3} d v

(\partial)/(\partial x)(x^3+axy^2)

\frac{\partial}{\partial x} (x^{3} + a x y^{2})

limit as x approaches-infinity of (4arctan(8x))/(e^x+2)

x \to - \infty lim (\frac{4 arctan ( 8 x )}{e ^{x} + 2})

y^{^{'}} - 2 y = 3 e^{2 x}