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Beliebt Rechnen >

derivative of ln((4x^2/(x-6)))

Lösung

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

Lösung

\frac{x - 12}{x ( x - 6 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{4 x ^{2}}{x - 6}))

Wende die Kettenregel an:

\frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \frac{d}{d x} (\frac{4 x ^{2}}{x - 6})

\frac{d}{d x} (\frac{4 x ^{2}}{x - 6}) = \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

= \frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}}

Vereinfache

\frac{1}{\frac{4 x ^{2}}{x - 6}} \cdot \frac{4 ( x ^{2} - 12 x )}{( x - 6 ) ^{2}} : \frac{x - 12}{x ( x - 6 )}

= \frac{x - 12}{x ( x - 6 )}

Graph

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