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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(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

Vereinfache

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 (X + Y) (X + Y^{^{'}})

e x p an d \frac{( x ^{2} + 1 ) ^{3}}{6}

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

e x p an d - \frac{5 x ( 4 x - 14 )}{3}

e x p an d \frac{3 ( s + x )}{s ( s + 1 )}