derivative of arcsin(x/(10))

解

\frac{d}{d x} (arcsin (\frac{x}{10}))

\frac{1}{100 - x ^{2}}

解答ステップ

\frac{d}{d x} (arcsin (\frac{x}{10}))

連鎖法則を適用:

\frac{1}{1 - ( \frac{x}{10} ) ^{2}} \frac{d}{d x} (\frac{x}{10})

= \frac{1}{1 - ( \frac{x}{10} ) ^{2}} \frac{d}{d x} (\frac{x}{10})

\frac{d}{d x} (\frac{x}{10}) = \frac{1}{10}

= \frac{1}{1 - ( \frac{x}{10} ) ^{2}} \cdot \frac{1}{10}

簡素化

\frac{1}{1 - ( \frac{x}{10} ) ^{2}} \cdot \frac{1}{10} : \frac{1}{100 - x ^{2}}

= \frac{1}{100 - x ^{2}}