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人気のある微分積分 >

derivative of-4xy

解

\frac{d}{d x} (- 4 x y)

解

- 4 (y + x \frac{d y}{d x})

解答ステップ

\frac{d}{d x} (- 4 x y)

定数を除去:

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

= - 4 \frac{d}{d x} (x y)

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y

= - 4 (\frac{d x}{d x} y + \frac{d y}{d x} x)

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

= - 4 (1 \cdot y + \frac{d y}{d x} x)

簡素化

= - 4 (y + x \frac{d y}{d x})

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