derivative of 4cos(x/2)

解

\frac{d}{d x} (4 cos (\frac{x}{2}))

- 2 sin (\frac{x}{2})

解答ステップ

\frac{d}{d x} (4 cos (\frac{x}{2}))

定数を除去:

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

= 4 \frac{d}{d x} (cos (\frac{x}{2}))

連鎖法則を適用:

- sin (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

= - sin (\frac{x}{2}) \frac{d}{d x} (\frac{x}{2})

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

= 4 (- sin (\frac{x}{2}) \frac{1}{2})

簡素化

4 (- sin (\frac{x}{2}) \frac{1}{2}) : - 2 sin (\frac{x}{2})

= - 2 sin (\frac{x}{2})