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人気のある微分積分 >

derivative 5sin(1/5 x)

解

導関数

5 sin (\frac{1}{5} x)

解

cos (\frac{x}{5})

解答ステップ

\frac{d}{d x} (5 sin (\frac{1}{5} x))

簡素化

5 sin (\frac{1}{5} x) : 5 sin (\frac{x}{5})

= \frac{d}{d x} (5 sin (\frac{x}{5}))

定数を除去:

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

= 5 \frac{d}{d x} (sin (\frac{x}{5}))

連鎖法則を適用:

cos (\frac{x}{5}) \frac{d}{d x} (\frac{x}{5})

= cos (\frac{x}{5}) \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= 5 cos (\frac{x}{5}) \frac{1}{5}

簡素化

5 cos (\frac{x}{5}) \frac{1}{5} : cos (\frac{x}{5})

= cos (\frac{x}{5})

グラフ

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