derivative of-7sin(x/7)

解

\frac{d}{d x} (- 7 sin (\frac{x}{7}))

- cos (\frac{x}{7})

解答ステップ

\frac{d}{d x} (- 7 sin (\frac{x}{7}))

定数を除去:

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

= - 7 \frac{d}{d x} (sin (\frac{x}{7}))

連鎖法則を適用:

cos (\frac{x}{7}) \frac{d}{d x} (\frac{x}{7})

= cos (\frac{x}{7}) \frac{d}{d x} (\frac{x}{7})

\frac{d}{d x} (\frac{x}{7}) = \frac{1}{7}

= - 7 cos (\frac{x}{7}) \frac{1}{7}

簡素化

- 7 cos (\frac{x}{7}) \frac{1}{7} : - cos (\frac{x}{7})

= - cos (\frac{x}{7})