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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (-1)/x

\int \frac{- 1}{x} d x

y (x + 7) + y^{^{'}} = 0

derivative of tan(5x+2)

\frac{d}{d x} (tan (5 x + 2))

derivative of x^3*e^{-x}

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

derivative of x^4-8x^3+22x^2-24x+9

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