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Beliebt Rechnen >

derivative e^yy^e

Lösung

ableitung von

e^{y} y^{e}

Lösung

e^{y} y^{e} + e^{1 + y} y^{e - 1}

Schritte zur Lösung

\frac{d}{d y} (e^{y} y^{e})

Wende die Produktregel an:

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

f = e^{y}, g = y^{e}

= \frac{d}{d y} (e^{y}) y^{e} + \frac{d}{d y} (y^{e}) e^{y}

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

\frac{d}{d y} (y^{e}) = e y^{e - 1}

= e^{y} y^{e} + e y^{e - 1} e^{y}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

e e^{y} = e^{1 + y}

= e^{y} y^{e} + e^{1 + y} y^{e - 1}

Graph

Beliebte Beispiele

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