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Beliebt Rechnen >

derivative of ln(2x^3-x^2)

Lösung

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

Lösung

\frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 x ^{3} - x ^{2}} (6 x^{2} - 2 x) : \frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

= \frac{2 ( 3 x - 1 )}{x ( 2 x - 1 )}

Graph

Beliebte Beispiele

derivative of 4/(3x^3)

\frac{d}{d x} (\frac{4}{3 x ^{3}})

integral of x^3sqrt(x^2-5)

\int x^{3} x^{2} - 5 d x

(dy)/(dx)-3/x y=x^3

\frac{d y}{d x} - \frac{3}{x} y = x^{3}

sum from k=1 to infinity of 0

k = 1 \sum \infty 0

derivative x^3+9x^2+35x+14

d er i v a t i v e x^{3} + 9 x^{2} + 35 x + 14