derivative t^2e^t

Lösung

ableitung von

t^{2} e^{t}

2 t e^{t} + e^{t} t^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = t^{2}, g = e^{t}

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

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

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

= 2 t e^{t} + e^{t} t^{2}

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