derivative of sin(marcsin(x))

解

\frac{d}{d x} (sin (m arcsin (x)))

\frac{m cos ( m arcsin ( x ) )}{1 - x ^{2}}

解答ステップ

\frac{d}{d x} (sin (m arcsin (x)))

連鎖法則を適用:

cos (m arcsin (x)) \frac{d}{d x} (m arcsin (x))

= cos (m arcsin (x)) \frac{d}{d x} (m arcsin (x))

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

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

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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