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人気のある微分積分 >

derivative y=5x^2-10x-6x^{-2}

解

導関数

y = 5 x^{2} - 10 x - 6 x^{- 2}

解

10 x - 10 + \frac{12}{x ^{3}}

解答ステップ

\frac{d}{d x} (5 x^{2} - 10 x - 6 x^{- 2})

和/差の法則を適用:

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

= \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (10 x) - \frac{d}{d x} (6 x^{- 2})

\frac{d}{d x} (5 x^{2}) = 10 x

\frac{d}{d x} (10 x) = 10

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

= 10 x - 10 - (- \frac{12}{x ^{3}})

簡素化

= 10 x - 10 + \frac{12}{x ^{3}}

グラフ

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