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Beliebt Rechnen >

derivative f(x)=ln(x^2-18x)

Lösung

ableitung von

f (x) = ln (x^{2} - 18 x)

Lösung

\frac{2 x - 18}{x ^{2} - 18 x}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} - 18 x))

Wende die Kettenregel an:

\frac{1}{x ^{2} - 18 x} \frac{d}{d x} (x^{2} - 18 x)

= \frac{1}{x ^{2} - 18 x} \frac{d}{d x} (x^{2} - 18 x)

\frac{d}{d x} (x^{2} - 18 x) = 2 x - 18

= \frac{1}{x ^{2} - 18 x} (2 x - 18)

Vereinfache

\frac{1}{x ^{2} - 18 x} (2 x - 18) : \frac{2 x - 18}{x ^{2} - 18 x}

= \frac{2 x - 18}{x ^{2} - 18 x}

Graph

Beliebte Beispiele

derivative of (x^4)

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

derivative of (-x^3/3)

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

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

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

derivative ln(7-6x)

d er i v a t i v e ln (7 - 6 x)

steigung (32,-39),(17,6)

s l o p e (32, - 39), (17, 6)