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Beliebt Rechnen >

derivative of 2^{x+1}

Lösung

\frac{d}{d x} (2^{x + 1})

Lösung

ln (2) \cdot 2^{x + 1}

Schritte zur Lösung

\frac{d}{d x} (2^{x + 1})

Wende Exponentenregel an:

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

2^{x + 1} = e^{(x + 1) l n (2)}

= \frac{d}{d x} (e^{(x + 1) l n (2)})

Wende die Kettenregel an:

e^{(x + 1) l n (2)} \frac{d}{d x} ((x + 1) ln (2))

= e^{(x + 1) l n (2)} \frac{d}{d x} ((x + 1) ln (2))

\frac{d}{d x} ((x + 1) ln (2)) = ln (2)

= e^{(x + 1) l n (2)} ln (2)

e^{(x + 1) l n (2)} = 2^{x + 1}

= ln (2) \cdot 2^{x + 1}

Graph

Beliebte Beispiele

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