derivative arcsin(6/7 x)

解

導関数

arcsin (\frac{6}{7} x)

\frac{6}{49 - 36 x ^{2}}

解答ステップ

\frac{d}{d x} (arcsin (\frac{6}{7} x))

簡素化

arcsin (\frac{6}{7} x) : arcsin (\frac{6 x}{7})

= \frac{d}{d x} (arcsin (\frac{6 x}{7}))

連鎖法則を適用:

\frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \frac{d}{d x} (\frac{6 x}{7})

= \frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \frac{d}{d x} (\frac{6 x}{7})

\frac{d}{d x} (\frac{6 x}{7}) = \frac{6}{7}

= \frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \cdot \frac{6}{7}

簡素化

\frac{1}{1 - ( \frac{6 x}{7} ) ^{2}} \cdot \frac{6}{7} : \frac{6}{49 - 36 x ^{2}}

= \frac{6}{49 - 36 x ^{2}}