d/(dt)((x)(sin(2t)))

解答

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

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

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (2 t)

= \frac{d x}{d t} sin (2 t) + \frac{d}{d t} (sin (2 t)) x

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

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

f a c t or A x^{3} e^{- 2 x} + B x^{2} e^{- 2 x}

f a c t or \frac{x}{x + 1 - 1}

f a c t or 2 x^{2} + 4 x + 2 + x + 1

d ec t o f r a c 6.4

f a c t or 2 m^{2} n - mn p - 6 m + 3 p