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Beliebt Rechnen >

derivative 2^{x-1}

Lösung

ableitung von

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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derivative of sqrt(3)cos(4x+sin(4x))

\frac{d}{d x} (3 cos (4 x) + sin (4 x))