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人気のある微分積分 >

derivative of x-arctan(x)

解

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

解

1 - \frac{1}{x ^{2} + 1}

解答ステップ

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

和/差の法則を適用:

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

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

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

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

= 1 - \frac{1}{x ^{2} + 1}

グラフ

人気の例

(\partial)/(\partial x)(ln(x^2+y))

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

integral of (2+u)/u

\int \frac{2 + u}{u} d u

derivative y=x^3(3-x^2)

d er i v a t i v e y = x^{3} (3 - x^{2})

(\partial)/(\partial x)(sin(pi(4x-2y)))

\frac{\partial}{\partial x} (sin (π (4 x - 2 y)))

勾配 y=3x^2,\at x=1

s l o p e y = 3 x^{2}, at x = 1