derivative 5^{x^2}

Lösung

ableitung von

5^{x^{2}}

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

Schritte zur Lösung

\frac{d}{d x} (5^{x^{2}})

Wende Exponentenregel an:

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

5^{x^{2}} = e^{x^{2} l n (5)}

= \frac{d}{d x} (e^{x^{2} l n (5)})

Wende die Kettenregel an:

e^{x^{2} l n (5)} \frac{d}{d x} (x^{2} ln (5))

= e^{x^{2} l n (5)} \frac{d}{d x} (x^{2} ln (5))

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

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

e^{x^{2} l n (5)} = 5^{x^{2}}

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

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