derivative of arcsin(x/6)

解

\frac{d}{d x} (arcsin (\frac{x}{6}))

\frac{1}{36 - x ^{2}}

解答ステップ

\frac{d}{d x} (arcsin (\frac{x}{6}))

連鎖法則を適用:

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6}

簡素化

\frac{1}{1 - ( \frac{x}{6} ) ^{2}} \cdot \frac{1}{6} : \frac{1}{36 - x ^{2}}

= \frac{1}{36 - x ^{2}}