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Beliebt Rechnen >

derivative of 3x^{5x}

Lösung

\frac{d}{d x} (3 x^{5 x})

Lösung

15 x^{5 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (3 x^{5 x})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (x^{5 x})

Wende Exponentenregel an:

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

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

= 3 \frac{d}{d x} (e^{5 x l n (x)})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x ln (x)) = 5 (ln (x) + 1)

= 3 e^{5 x l n (x)} \cdot 5 (ln (x) + 1)

Vereinfache

3 e^{5 x l n (x)} \cdot 5 (ln (x) + 1) : 15 x^{5 x} (ln (x) + 1)

= 15 x^{5 x} (ln (x) + 1)

Graph

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