d/(dt)((x)(tcos(t)))

解答

\frac{d}{d t} ((x) (t cos (t)))

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

求解步骤

\frac{d}{d t} ((x) (t cos (t)))

使用微分乘法定则:

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

f = x, g = t cos (t)

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

\frac{d}{d t} (t cos (t)) = cos (t) - t sin (t)

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

f a c t or 3 a^{2} - 9 ab - 5 a c + 15 b c

f a c t or (x + 3)^{3} + 1

f a c t or \frac{x ^{2} - 2 x}{x}

f a c t or 4 x^{2} - (x + 2)

f a c t or e^{j θ} - e^{- j θ}