derivative of 1/4 cos(x/4)

解

\frac{d}{d x} (\frac{1}{4} cos (\frac{x}{4}))

- \frac{1}{16} sin (\frac{x}{4})

解答ステップ

\frac{d}{d x} (\frac{1}{4} cos (\frac{x}{4}))

定数を除去:

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

= \frac{1}{4} \frac{d}{d x} (cos (\frac{x}{4}))

連鎖法則を適用:

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

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

\frac{d}{d x} (\frac{x}{4}) = \frac{1}{4}

= \frac{1}{4} (- sin (\frac{x}{4}) \frac{1}{4})

簡素化

\frac{1}{4} (- sin (\frac{x}{4}) \frac{1}{4}) : - \frac{1}{16} sin (\frac{x}{4})

= - \frac{1}{16} sin (\frac{x}{4})