derivative ln(3x^3+6x^2+2x+6)

Lösung

ableitung von

ln (3 x^{3} + 6 x^{2} + 2 x + 6)

\frac{9 x ^{2} + 12 x + 2}{3 x ^{3} + 6 x ^{2} + 2 x + 6}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x^{3} + 6 x^{2} + 2 x + 6) = 9 x^{2} + 12 x + 2

= \frac{1}{3 x ^{3} + 6 x ^{2} + 2 x + 6} (9 x^{2} + 12 x + 2)

Vereinfache

\frac{1}{3 x ^{3} + 6 x ^{2} + 2 x + 6} (9 x^{2} + 12 x + 2) : \frac{9 x ^{2} + 12 x + 2}{3 x ^{3} + 6 x ^{2} + 2 x + 6}

= \frac{9 x ^{2} + 12 x + 2}{3 x ^{3} + 6 x ^{2} + 2 x + 6}

x y^{2} y^{^{'}} = x + 9

\int x^{n} a x^{n + 1} + b d x

in v erse l a pl a ce \frac{s ^{2} - s + 1}{( s + 1 ) ^{2}}

\int_{0}^{1} 2 π (x + 10) x^{2} d x

d er i v a t i v e ln ∣ x ∣