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Beliebt Rechnen >

derivative t^2(5t+9)^3

Lösung

ableitung von

t^{2} (5 t + 9)^{3}

Lösung

2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}

Schritte zur Lösung

\frac{d}{d t} (t^{2} (5 t + 9)^{3})

Wende die Produktregel an:

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

f = t^{2}, g = (5 t + 9)^{3}

= \frac{d}{d t} (t^{2}) (5 t + 9)^{3} + \frac{d}{d t} ((5 t + 9)^{3}) t^{2}

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

\frac{d}{d t} ((5 t + 9)^{3}) = 15 (5 t + 9)^{2}

= 2 t (5 t + 9)^{3} + 15 (5 t + 9)^{2} t^{2}

Graph

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