derivative of 6^{(4-3x})

Lösung

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

- ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{(4 - 3 x) l n (6)} (- 3 ln (6)) : - ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

= - ln (6) \cdot 2^{4 - 3 x} \cdot 3^{- 3 x + 5}

\int_{1}^{4} (x^{2} - 3 x) d x

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