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Beliebt Rechnen >

d/(dz)(9z^2e^z)

Lösung

\frac{d}{d z} (9 z^{2} e^{z})

Lösung

9 (2 z e^{z} + e^{z} z^{2})

Schritte zur Lösung

\frac{d}{d z} (9 z^{2} e^{z})

Entferne die Konstante:

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

= 9 \frac{d}{d z} (z^{2} e^{z})

Wende die Produktregel an:

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

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

= 9 (\frac{d}{d z} (z^{2}) e^{z} + \frac{d}{d z} (e^{z}) z^{2})

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

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

= 9 (2 z e^{z} + e^{z} z^{2})

Graph

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