derivative of 2sin(1/2 x)

解

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

cos (\frac{x}{2})

解答ステップ

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

簡素化

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

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

定数を除去:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

2 cos (\frac{x}{2}) \frac{1}{2} : cos (\frac{x}{2})

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