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Beliebt Rechnen >

derivative f(x)=x^{3x}

Lösung

ableitung von

f (x) = x^{3 x}

Lösung

3 x^{3 x} (ln (x) + 1)

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + 1)

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

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

= 3 x^{3 x} (ln (x) + 1)

Graph

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