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Beliebt Rechnen >

derivative of ln(x^2-9x+1)

Lösung

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

Lösung

\frac{2 x - 9}{x ^{2} - 9 x + 1}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{2} - 9 x + 1))

Wende die Kettenregel an:

\frac{1}{x ^{2} - 9 x + 1} \frac{d}{d x} (x^{2} - 9 x + 1)

= \frac{1}{x ^{2} - 9 x + 1} \frac{d}{d x} (x^{2} - 9 x + 1)

\frac{d}{d x} (x^{2} - 9 x + 1) = 2 x - 9

= \frac{1}{x ^{2} - 9 x + 1} (2 x - 9)

Vereinfache

\frac{1}{x ^{2} - 9 x + 1} (2 x - 9) : \frac{2 x - 9}{x ^{2} - 9 x + 1}

= \frac{2 x - 9}{x ^{2} - 9 x + 1}

Graph

Beliebte Beispiele

integral of 1/(sqrt(x^2-6x+10))

\int \frac{1}{x ^{2} - 6 x + 10} d x

integral of x^2-2x-15

\int x^{2} - 2 x - 15 d x

derivative of (2e^x/(5x))

\frac{d}{d x} (\frac{2 e ^{x}}{5 x})

integral of sin(2θ)cos^4(2θ)

\int sin (2 θ) cos^{4} (2 θ) d θ

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\int \frac{1}{sec ( θ )} d θ