derivative f(x)=(x+2)^x

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

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