(\partial)/(\partial x)(x^{xy})

Lösung

\frac{\partial}{\partial x} (x^{x y})

y x^{x y} (ln (x) + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{x y})

Behandle

y

als Konstante

Wende Exponentenregel an:

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

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

= \frac{\partial}{\partial x} (e^{x y l n (x)})

Wende die Kettenregel an:

e^{x y l n (x)} \frac{\partial}{\partial x} (x y ln (x))

= e^{x y l n (x)} \frac{\partial}{\partial x} (x y ln (x))

\frac{\partial}{\partial x} (x y ln (x)) = y (ln (x) + 1)

= e^{x y l n (x)} y (ln (x) + 1)

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

= y x^{x y} (ln (x) + 1)

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