derivative 3sin^2(x)

解

導関数

3 sin^{2} (x)

3 sin (2 x)

解答ステップ

\frac{d}{d x} (3 sin^{2} (x))

定数を除去:

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

= 3 \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)

= 3 \cdot 2 sin (x) cos (x)

簡素化

3 \cdot 2 sin (x) cos (x) : 3 sin (2 x)

= 3 sin (2 x)