d/(dt)((x)(x-1)(1-2x))

解答

\frac{d}{d t} ((t) (t - 1) (1 - 2 t))

- 6 t^{2} + 6 t - 1

求解步骤

\frac{d}{d t} ((t) (t - 1) (1 - 2 t))

使用微分乘法定则:

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

f = t, g = (t - 1) (1 - 2 t)

= \frac{d t}{d t} (t - 1) (1 - 2 t) + \frac{d}{d t} ((t - 1) (1 - 2 t)) t

\frac{d t}{d t} = 1

\frac{d}{d t} ((t - 1) (1 - 2 t)) = - 4 t + 3

= 1 \cdot (t - 1) (1 - 2 t) + (- 4 t + 3) t

化简

1 \cdot (t - 1) (1 - 2 t) + (- 4 t + 3) t : - 6 t^{2} + 6 t - 1

= - 6 t^{2} + 6 t - 1

e x p an d 3^{(- x - 1)}

s im pl i f y (\frac{197}{193} - 0.25 (\frac{394}{193})) \cdot 1 0^{3}

e x p an d \frac{( 6 x + 54 ) ( 2 x + 18 )}{( 25 x + 35 ) ( 5 x + 7 )}

e x p an d (1 + sin (θ))^{2} + cos^{2} (θ)

e x p an d (e^{x} - 4) \cdot (e^{x} + 12)