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Beliebt Rechnen >

derivative 3*2^{2x+1}

Lösung

ableitung von

3 \cdot 2^{2 x + 1}

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (3 \cdot 2^{2 x + 1})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (2^{2 x + 1})

Wende Exponentenregel an:

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

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

= 3 \frac{d}{d x} (e^{(2 x + 1) l n (2)})

Wende die Kettenregel an:

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

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

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

= 3 e^{(2 x + 1) l n (2)} \cdot 2 ln (2)

Vereinfache

3 e^{(2 x + 1) l n (2)} \cdot 2 ln (2) : 3 ln (2) \cdot 2^{2 x + 2}

= 3 ln (2) \cdot 2^{2 x + 2}

Graph

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