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Beliebt Rechnen >

derivative of ln(sqrt(x(1-x)))

Lösung

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

Lösung

\frac{1 - 2 x}{2 x ( 1 - x )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1 - 2 x}{2 x ( 1 - x )}

Graph

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derivative ln(X^{1/2})

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