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Beliebt Rechnen >

derivative (1+sqrt(t))(2t^2-7)

Lösung

ableitung von

(1 + t) (2 t^{2} - 7)

Lösung

\frac{10 t ^{2} + 8 t t - 7}{2 t}

Schritte zur Lösung

\frac{d}{d t} ((1 + t) (2 t^{2} - 7))

Wende die Produktregel an:

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

f = 1 + t, g = 2 t^{2} - 7

= \frac{d}{d t} (1 + t) (2 t^{2} - 7) + \frac{d}{d t} (2 t^{2} - 7) (1 + t)

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

\frac{d}{d t} (2 t^{2} - 7) = 4 t

= \frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t)

Vereinfache

\frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t) : \frac{10 t ^{2} + 8 t t - 7}{2 t}

= \frac{10 t ^{2} + 8 t t - 7}{2 t}

Graph

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