derivative of 1/2 (1-cos(2x))

解

\frac{d}{d x} (\frac{1}{2} (1 - cos (2 x)))

sin (2 x)

解答ステップ

\frac{d}{d x} (\frac{1}{2} (1 - cos (2 x)))

簡素化

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

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

連鎖法則を適用:

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

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

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

= 2 sin (x) cos (x)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

= sin (2 x)