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人気のある微分積分 >

derivative (12)/(x^2(x-3))

解

導関数

\frac{12}{x ^{2} ( x - 3 )}

解

- \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{12}{x ^{2} ( x - 3 )})

定数を除去:

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

= 12 \frac{d}{d x} (\frac{1}{x ^{2} ( x - 3 )})

指数の規則を適用する:

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

= 12 \frac{d}{d x} ((x^{2} (x - 3))^{- 1})

連鎖法則を適用:

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

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

\frac{d}{d x} (x^{2} (x - 3)) = 3 x^{2} - 6 x

= 12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x))

簡素化

12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x)) : - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

= - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

グラフ

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