derivative y=ln(1/(xsqrt(x-10)))

Lösung

ableitung von

y = ln (\frac{1}{x x - 10})

- \frac{3 x - 20}{2 x ( x - 10 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{1}{x x - 10}))

Vereinfache

ln (\frac{1}{x x - 10}) : - ln (x x - 10)

= \frac{d}{d x} (- ln (x x - 10))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (ln (x x - 10))

Wende die Kettenregel an:

\frac{1}{x x - 10} \frac{d}{d x} (x x - 10)

= \frac{1}{x x - 10} \frac{d}{d x} (x x - 10)

\frac{d}{d x} (x x - 10) = \frac{3 x - 20}{2 x - 10}

= - \frac{1}{x x - 10} \cdot \frac{3 x - 20}{2 x - 10}

Vereinfache

- \frac{1}{x x - 10} \cdot \frac{3 x - 20}{2 x - 10} : - \frac{3 x - 20}{2 x ( x - 10 )}

= - \frac{3 x - 20}{2 x ( x - 10 )}

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