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人気のある微分積分 >

derivative of 3e^{1-x^2}

解

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

解

- 6 e^{1 - x^{2}} x

解答ステップ

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= 3 e^{1 - x^{2}} (- 2 x)

簡素化

= - 6 e^{1 - x^{2}} x

グラフ

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