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Beliebt Rechnen >

derivative of 3^{-6x+6}

Lösung

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

Lösung

- 2 ln (3) \cdot 3^{- 6 x + 7}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

e^{(- 6 x + 6) l n (3)} (- 6 ln (3)) : - 2 ln (3) \cdot 3^{- 6 x + 7}

= - 2 ln (3) \cdot 3^{- 6 x + 7}

Graph

Beliebte Beispiele

f^'(x)=3x^2(8-x^{-3})

f^{^{'}} (x) = 3 x^{2} (8 - x^{- 3})

integral from 0 to 1 of 5^{2x}

\int_{0}^{1} 5^{2 x} d x

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\int_{0}^{1} x^{3} + x d x

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n = 0 \sum \infty \frac{x ^{n}}{n ^{2}}

(d^2)/(dx^2)(1/(1-x))

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