derivative y=x^{x^3}

Lösung

ableitung von

y = x^{x^{3}}

x^{x^{3}} (3 x^{2} ln (x) + x^{2})

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

= e^{x^{3} l n (x)} (3 x^{2} ln (x) + x^{2})

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

= x^{x^{3}} (3 x^{2} ln (x) + x^{2})

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