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Beliebt Rechnen >

derivative of ln(2x^3+8x)

Lösung

\frac{d}{d x} (ln (2 x^{3} + 8 x))

Lösung

\frac{3 x ^{2} + 4}{x ( x ^{2} + 4 )}

Schritte zur Lösung

\frac{d}{d x} (ln (2 x^{3} + 8 x))

Wende die Kettenregel an:

\frac{1}{2 x ^{3} + 8 x} \frac{d}{d x} (2 x^{3} + 8 x)

= \frac{1}{2 x ^{3} + 8 x} \frac{d}{d x} (2 x^{3} + 8 x)

\frac{d}{d x} (2 x^{3} + 8 x) = 6 x^{2} + 8

= \frac{1}{2 x ^{3} + 8 x} (6 x^{2} + 8)

Vereinfache

\frac{1}{2 x ^{3} + 8 x} (6 x^{2} + 8) : \frac{3 x ^{2} + 4}{x ( x ^{2} + 4 )}

= \frac{3 x ^{2} + 4}{x ( x ^{2} + 4 )}

Graph

Beliebte Beispiele

integral of 8^{2x+6}

\int 8^{2 x + 6} d x

inverselaplace 8/(0.65s+1)

in v erse l a pl a ce \frac{8}{0.65 s + 1}

derivative x/(1+x^2)

d er i v a t i v e \frac{x}{1 + x ^{2}}

integral of (3x-4)/(x^2-x-6)

\int \frac{3 x - 4}{x ^{2} - x - 6} d x

derivative of 6sqrt(x)-3x

\frac{d}{d x} (6 x - 3 x)