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Beliebt Rechnen >

derivative (x^2+x)^x

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

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