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人気のある微分積分 >

derivative (-6x)/(x^2+1)

解

導関数

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

解

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

解答ステップ

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

簡素化

\frac{- 6 x}{x ^{2} + 1} : - \frac{6 x}{x ^{2} + 1}

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

定数を除去:

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

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

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

簡素化

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

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

グラフ

人気の例

derivative f(x)=4x^3-18x^2

d er i v a t i v e f (x) = 4 x^{3} - 18 x^{2}

limit as x approaches-1 of x^5-1

x \to - 1 lim (x^{5} - 1)

derivative of 6pix^2

\frac{d}{d x} (6 π x^{2})

integral of (1+2t^3)/t

\int \frac{1 + 2 t ^{3}}{t} d t

y^{^{''}} = a^{2} y