derivative of sin^3(3x-1)

解

\frac{d}{d x} (sin^{3} (3 x - 1))

9 sin^{2} (3 x - 1) cos (3 x - 1)

解答ステップ

\frac{d}{d x} (sin^{3} (3 x - 1))

連鎖法則を適用:

3 (sin (3 x - 1))^{2} \frac{d}{d x} (sin (3 x - 1))

= 3 (sin (3 x - 1))^{2} \frac{d}{d x} (sin (3 x - 1))

\frac{d}{d x} (sin (3 x - 1)) = cos (3 x - 1) \cdot 3

= 3 (sin (3 x - 1))^{2} cos (3 x - 1) \cdot 3

簡素化

= 9 sin^{2} (3 x - 1) cos (3 x - 1)