d/(dt)((x)(e^t(sin(t)+cos(t))))

解答

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

2 e^{t} x cos (t)

求解步骤

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

将

x

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分乘法定则:

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

f = e^{t}, g = sin (t) + cos (t)

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

\frac{d}{d t} (e^{t}) = e^{t}

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

= x (e^{t} (sin (t) + cos (t)) + (cos (t) - sin (t)) e^{t})

乘开

e^{t} (sin (t) + cos (t)) + (cos (t) - sin (t)) e^{t} : 2 e^{t} cos (t)

= 2 e^{t} x cos (t)

e x p an d [(x - 4) (2 x + 1)] x

e x p an d \frac{s ^{3} + 17}{s ( s ^{2} + 10 s + 34 )}

e x p an d (2 x^{3} + 4 x^{2} - 7 x + 3) (2 x - 4)^{'}

e x p an d \frac{1}{( z - 2 ) ( x - 3 )}

e x p an d (1 + csc (a)) (1 csc (a) = - cot^{2} (a))