derivative y=sin^3(1-2x)

解答

导数

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

- 6 sin^{2} (1 - 2 x) cos (1 - 2 x)

求解步骤

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

使用连锁律:

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

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

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

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

化简

= - 6 sin^{2} (1 - 2 x) cos (1 - 2 x)

d er i v a t i v e (x^{2} + 1)^{\frac{1}{2}} - 1

d er i v a t i v e (x + 1) (x - 2)^{2}

d er i v a t i v e f (x) = cos^{4} (x) - 2 x^{2}

d er i v a t i v e (4 u)^{3}

d er i v a t i v e 5 x - 1