derivative sin^3(2t)

解答

导数

sin^{3} (2 t)

6 sin^{2} (2 t) cos (2 t)

求解步骤

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

使用连锁律:

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

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

\frac{d}{d t} (sin (2 t)) = cos (2 t) \cdot 2

= 3 (sin (2 t))^{2} cos (2 t) \cdot 2

化简

= 6 sin^{2} (2 t) cos (2 t)

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