d/(dt)((x)(cos(t)+tsin(t)))

解答

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

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

求解步骤

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

使用微分乘法定则:

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

f = x, g = cos (t) + t sin (t)

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

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

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

e x p an d 2 (x^{2} + 2 x - 5)^{3}

e x p an d x (1 - 3 x)

e x p an d \frac{( 8 x ^{2} + 13 )}{( x ^{2} + 1 ) ( x + 1 )}

s im pl i f y 1 + \frac{3.3 ( s + 6 ) ( s + 10.75 )}{( s + 2 ) ( s + 3 ) ( s + 5 )}

e x p an d (3 (x) + 2 (h, y) - 5) - (3 (x) + 2 (y) - 5)