derivative of sqrt(x(1-x))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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