derivative y=x^{x^2}

Lösung

ableitung von

y = x^{x^{2}}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

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