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 \frac{3 - x}{( x + 2 ) ( x - 2 )}

e x p an d ln (x) (x + 2) (x + 1)

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

e x p an d \frac{15 ( e - 1 )}{2 e}

\frac{\partial}{\partial t} ((z) (x^{2} + y^{5}))