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Beliebt Rechnen >

derivative of 6^{3x-4}

Lösung

\frac{d}{d x} (6^{3 x - 4})

Lösung

ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

Schritte zur Lösung

\frac{d}{d x} (6^{3 x - 4})

Wende Exponentenregel an:

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

6^{3 x - 4} = e^{(3 x - 4) l n (6)}

= \frac{d}{d x} (e^{(3 x - 4) l n (6)})

Wende die Kettenregel an:

e^{(3 x - 4) l n (6)} \frac{d}{d x} ((3 x - 4) ln (6))

= e^{(3 x - 4) l n (6)} \frac{d}{d x} ((3 x - 4) ln (6))

\frac{d}{d x} ((3 x - 4) ln (6)) = 3 ln (6)

= e^{(3 x - 4) l n (6)} \cdot 3 ln (6)

Vereinfache

e^{(3 x - 4) l n (6)} \cdot 3 ln (6) : ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

= ln (6) \cdot 2^{3 x - 4} \cdot 3^{3 x - 3}

Graph

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