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Beliebt Rechnen >

derivative of x^{8e^{5x}}

Lösung

\frac{d}{d x} (x^{8 e^{5 x}})

Lösung

8 x^{8 e^{5 x}} (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{8 e^{5 x}})

Wende Exponentenregel an:

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

x^{8 e^{5 x}} = e^{8 e^{5 x} l n (x)}

= \frac{d}{d x} (e^{8 e^{5 x} l n (x)})

Wende die Kettenregel an:

e^{8 e^{5 x} l n (x)} \frac{d}{d x} (8 e^{5 x} ln (x))

= e^{8 e^{5 x} l n (x)} \frac{d}{d x} (8 e^{5 x} ln (x))

\frac{d}{d x} (8 e^{5 x} ln (x)) = 8 (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

= e^{8 e^{5 x} l n (x)} \cdot 8 (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

e^{8 e^{5 x} l n (x)} = x^{8 e^{5 x}}

= 8 x^{8 e^{5 x}} (5 e^{5 x} ln (x) + \frac{e ^{5 x}}{x})

Graph

Beliebte Beispiele

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