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人気のある微分積分 >

derivative F(x)= 3/(1+x^2)

解

導関数

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

解

- \frac{6 x}{( 1 + x ^{2} ) ^{2}}

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

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

連鎖法則を適用:

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

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

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

= 3 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x)

簡素化

3 (- \frac{1}{( 1 + x ^{2} ) ^{2}} \cdot 2 x) : - \frac{6 x}{( 1 + x ^{2} ) ^{2}}

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

グラフ

人気の例

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\int 3 x - 5 d x

(\partial)/(\partial z)(x^2y)

\frac{\partial}{\partial z} (x^{2} y)

limit as x approaches pi of+(ln(sin(x)))

x \to π lim (+ (ln (sin (x))))

(\partial)/(\partial x)(x/(x^5-y^3))

\frac{\partial}{\partial x} (\frac{x}{x ^{5} - y ^{3}})

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