derivative of 4sin^2(3x)

解

\frac{d}{d x} (4 sin^{2} (3 x))

12 sin (6 x)

解答ステップ

\frac{d}{d x} (4 sin^{2} (3 x))

定数を除去:

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

= 4 \frac{d}{d x} (sin^{2} (3 x))

連鎖法則を適用:

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

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= 4 \cdot 2 sin (3 x) cos (3 x) \cdot 3

簡素化

4 \cdot 2 sin (3 x) cos (3 x) \cdot 3 : 12 sin (6 x)

= 12 sin (6 x)