derivative of arcsin({sqrt(((1-x)/2)}))

解

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

- \frac{1}{2 x + 1 1 - x}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{1}{2 x + 1 1 - x}