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Beliebt Rechnen >

derivative y=3^{x-1}

Lösung

ableitung von

y = 3^{x - 1}

Lösung

ln (3) \cdot 3^{x - 1}

Schritte zur Lösung

\frac{d}{d x} (3^{x - 1})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

3^{x - 1} = e^{(x - 1) l n (3)}

= \frac{d}{d x} (e^{(x - 1) l n (3)})

Wende die Kettenregel an:

e^{(x - 1) l n (3)} \frac{d}{d x} ((x - 1) ln (3))

= e^{(x - 1) l n (3)} \frac{d}{d x} ((x - 1) ln (3))

\frac{d}{d x} ((x - 1) ln (3)) = ln (3)

= e^{(x - 1) l n (3)} ln (3)

e^{(x - 1) l n (3)} = 3^{x - 1}

= ln (3) \cdot 3^{x - 1}

Graph

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