derivative arcsin(x/2)

解

導関数

arcsin (\frac{x}{2})

\frac{1}{4 - x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{1}{4 - x ^{2}}