derivative y=(sqrt(x))^{5x}

Lösung

ableitung von

y = (x)^{5 x}

5 (x)^{5 x} (ln (x) + \frac{1}{2})

Schritte zur Lösung

\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)}

= \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) + \frac{1}{2})

= e^{5 x l n (x)} \cdot 5 (ln (x) + \frac{1}{2})

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

= 5 (x)^{5 x} (ln (x) + \frac{1}{2})

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