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人気のある微分積分 >

derivative 8/(xsqrt(x^2-4))

解

導関数

\frac{8}{x x ^{2} - 4}

解

- \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

解答ステップ

\frac{d}{d x} (\frac{8}{x x ^{2} - 4})

定数を除去:

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

= 8 \frac{d}{d x} (\frac{1}{x x ^{2} - 4})

指数の規則を適用する:

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

= 8 \frac{d}{d x} ((x x^{2} - 4)^{- 1})

連鎖法則を適用:

- \frac{1}{( x x ^{2} - 4 ) ^{2}} \frac{d}{d x} (x x^{2} - 4)

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

\frac{d}{d x} (x x^{2} - 4) = \frac{2 x ^{2} - 4}{x ^{2} - 4}

= 8 (- \frac{1}{( x x ^{2} - 4 ) ^{2}} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4})

簡素化

8 (- \frac{1}{( x x ^{2} - 4 ) ^{2}} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4}) : - \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

= - \frac{8 ( 2 x ^{2} - 4 )}{x ^{2} ( x ^{2} - 4 ) x ^{2} - 4}

グラフ

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