derivative 5^{x^3}

Lösung

ableitung von

5^{x^{3}}

3 ln (5) \cdot 5^{x^{3}} x^{2}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{3} ln (5)) = 3 ln (5) x^{2}

= e^{x^{3} l n (5)} \cdot 3 ln (5) x^{2}

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

= 3 ln (5) \cdot 5^{x^{3}} x^{2}

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