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Beliebt Rechnen >

derivative of (ln(x)^5)

Lösung

\frac{d}{d x} ((ln (x))^{5})

Lösung

\frac{5 ln ^{4} ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{5})

Wende die Kettenregel an:

5 (ln (x))^{4} \frac{d}{d x} (ln (x))

= 5 (ln (x))^{4} \frac{d}{d x} (ln (x))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 5 (ln (x))^{4} \frac{1}{x}

Vereinfache

5 ln^{4} (x) \frac{1}{x} : \frac{5 ln ^{4} ( x )}{x}

= \frac{5 ln ^{4} ( x )}{x}

Graph

Beliebte Beispiele

integral of 8xe^{8x}

\int 8 x e^{8 x} d x

derivative ln^3(x)

d er i v a t i v e ln^{3} (x)

(dy}{dx}=\frac{(1-3y)^2)/x ,y(1)=1

\frac{d y}{d x} = \frac{( 1 - 3 y ) ^{2}}{x}, y (1) = 1

derivative of (x^2+1^2)

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

sum from n=0 to infinity of (n^2)/(n!)

n = 0 \sum \infty \frac{n ^{2}}{n !}