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Beliebt Rechnen >

derivative of 8^{x^3}

Lösung

\frac{d}{d x} (8^{x^{3}})

Lösung

9 ln (2) \cdot 8^{x^{3}} x^{2}

Schritte zur Lösung

\frac{d}{d x} (8^{x^{3}})

Wende Exponentenregel an:

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

8^{x^{3}} = e^{x^{3} l n (8)}

= \frac{d}{d x} (e^{x^{3} l n (8)})

Wende die Kettenregel an:

e^{x^{3} l n (8)} \frac{d}{d x} (x^{3} ln (8))

= e^{x^{3} l n (8)} \frac{d}{d x} (x^{3} ln (8))

\frac{d}{d x} (x^{3} ln (8)) = 9 ln (2) x^{2}

= e^{x^{3} l n (8)} \cdot 9 ln (2) x^{2}

e^{x^{3} l n (8)} = 8^{x^{3}}

= 9 ln (2) \cdot 8^{x^{3}} x^{2}

Graph

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