derivative of (x^2ln(x^{(55}))^{(1/3)})

Lösung

\frac{d}{d x} ((x^{2} ln (x^{(55)}))^{(\frac{1}{3})})

\frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} ln (x^{(55)}))^{(\frac{1}{3})})

Wende die Kettenregel an:

\frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} ln (x^{55}))

= \frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{2} ln (x^{55}))

\frac{d}{d x} (x^{2} ln (x^{55})) = 2 x ln (x^{55}) + 55 x

= \frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} (2 x ln (x^{55}) + 55 x)

Vereinfache

\frac{1}{3 ( x ^{2} ln ( x ^{55} ) ) ^{\frac{2}{3}}} (2 x ln (x^{55}) + 55 x) : \frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}

= \frac{5 5 ^{\frac{1}{3}} ( 2 ln ( x ) + 1 )}{3 x ^{\frac{1}{3}} ln ^{\frac{2}{3}} ( x )}