derivative 2sin(2v)-4sin^9(2v)

解答

导数

2 sin (2 v) - 4 sin^{9} (2 v)

4 cos (2 v) - 72 sin^{8} (2 v) cos (2 v)

求解步骤

\frac{d}{d v} (2 sin (2 v) - 4 sin^{9} (2 v))

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d v} (2 sin (2 v)) - \frac{d}{d v} (4 sin^{9} (2 v))

\frac{d}{d v} (2 sin (2 v)) = 4 cos (2 v)

\frac{d}{d v} (4 sin^{9} (2 v)) = 72 sin^{8} (2 v) cos (2 v)

= 4 cos (2 v) - 72 sin^{8} (2 v) cos (2 v)

\frac{d}{d x} (x e^{- y})

\int_{- 2}^{- 1} \frac{2}{x ^{2}} d x

(4 x + 2 x^{- 1} y + 2 x^{- 1} y^{2}) d x + (1 + 2 y) d y = 0

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

2 y d x - x d y = 0