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

解答

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

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

求解步骤

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

使用连锁律:

\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 )}

化简

\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 )}

d er i v a t i v e ln (X^{\frac{1}{2}})

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