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Beliebt Algebra >

derivative of (a(e^{ax^6}))

Lösung

\frac{d}{d x} ((a) (e^{a x^{6}}))

Lösung

6 a^{2} e^{a x^{6}} x^{5}

Schritte zur Lösung

\frac{d}{d x} ((a) (e^{a x^{6}}))

Entferne die Konstante:

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

= a \frac{d}{d x} (e^{a x^{6}})

Wende die Kettenregel an:

e^{a x^{6}} \frac{d}{d x} (a x^{6})

= e^{a x^{6}} \frac{d}{d x} (a x^{6})

\frac{d}{d x} (a x^{6}) = 6 a x^{5}

= a e^{a x^{6}} \cdot 6 a x^{5}

Vereinfache

a e^{a x^{6}} \cdot 6 a x^{5} : 6 a^{2} e^{a x^{6}} x^{5}

= 6 a^{2} e^{a x^{6}} x^{5}

Graph

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