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Beliebt Rechnen >

derivative f(t)=(t^2+3t+7)(3t^2+3)

Lösung

ableitung von

f (t) = (t^{2} + 3 t + 7) (3 t^{2} + 3)

Lösung

12 t^{3} + 27 t^{2} + 48 t + 9

Schritte zur Lösung

\frac{d}{d t} ((t^{2} + 3 t + 7) (3 t^{2} + 3))

Wende die Produktregel an:

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

f = t^{2} + 3 t + 7, g = 3 t^{2} + 3

= \frac{d}{d t} (t^{2} + 3 t + 7) (3 t^{2} + 3) + \frac{d}{d t} (3 t^{2} + 3) (t^{2} + 3 t + 7)

\frac{d}{d t} (t^{2} + 3 t + 7) = 2 t + 3

\frac{d}{d t} (3 t^{2} + 3) = 6 t

= (2 t + 3) (3 t^{2} + 3) + 6 t (t^{2} + 3 t + 7)

Vereinfache

(2 t + 3) (3 t^{2} + 3) + 6 t (t^{2} + 3 t + 7) : 12 t^{3} + 27 t^{2} + 48 t + 9

= 12 t^{3} + 27 t^{2} + 48 t + 9

Graph

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