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Beliebt Rechnen >

derivative y=ln(x+sqrt(x^2-6))

Lösung

ableitung von

y = ln (x + x^{2} - 6)

Lösung

\frac{1}{x ^{2} - 6}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1}{x ^{2} - 6}

Graph

Beliebte Beispiele

limit as x approaches 0 of ln(x^2+1)

x \to 0 lim (ln (x^{2} + 1))

y^{''}+3y^'-4y=0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0

integral of (cos(x))(tan(x))

\int (cos (x)) (tan (x)) d x

derivative of (4x^2-8x+8e^x)

\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{x})

integral of 1/((x-8)(x^2+25))

\int \frac{1}{( x - 8 ) ( x ^{2} + 25 )} d x