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

Lösung

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

3 t^{2} - 6 t + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 3 t^{2} - 6 t + 2

e x p an d \frac{x ^{2} ( 3 y - 2 x )}{6}

e x p an d \frac{( x ^{4} + 1 ) ^{2}}{x ^{4}}

e x p an d \frac{( - 3 x + 12 )}{x ( x - 3 )}

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

e x p an d \frac{( b s + a ) ^{2}}{s ^{3}}