d/(dw)((ln(w))^{(2w)})

Lösung

\frac{d}{d w} ((ln (w))^{(2 w)})

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

Schritte zur Lösung

\frac{d}{d w} ((ln (w))^{(2 w)})

Wende Exponentenregel an:

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

(ln (w))^{2 w} = e^{2 w l n (l n (w))}

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

Wende die Kettenregel an:

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

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

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

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

e^{2 w l n (l n (w))} = ln^{2 w} (w)

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

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