d/(dt)((x)(-2x(x-8)))

Lösung

\frac{d}{d t} ((t) (- 2 t (t - 8)))

- 2 (3 t^{2} - 16 t)

Schritte zur Lösung

\frac{d}{d t} ((t) (- 2 t (t - 8)))

Vereinfache

(t) (- 2 t (t - 8)) : - 2 t^{2} (t - 8)

= \frac{d}{d t} (- 2 t^{2} (t - 8))

Entferne die Konstante:

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

= - 2 \frac{d}{d t} (t^{2} (t - 8))

Wende die Produktregel an:

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

f = t^{2}, g = t - 8

= - 2 (\frac{d}{d t} (t^{2}) (t - 8) + \frac{d}{d t} (t - 8) t^{2})

\frac{d}{d t} (t^{2}) = 2 t

\frac{d}{d t} (t - 8) = 1

= - 2 (2 t (t - 8) + 1 \cdot t^{2})

Vereinfache

- 2 (2 t (t - 8) + 1 \cdot t^{2}) : - 2 (3 t^{2} - 16 t)

= - 2 (3 t^{2} - 16 t)

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p a r i t y t (- 5, - 6)