derivative of arcsin(sqrt(sin(11x)))

解

\frac{d}{d x} (arcsin (sin (11 x)))

\frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}

解答ステップ

\frac{d}{d x} (arcsin (sin (11 x)))

連鎖法則を適用:

\frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \frac{d}{d x} (sin (11 x))

= \frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \frac{d}{d x} (sin (11 x))

\frac{d}{d x} (sin (11 x)) = \frac{11 cos ( 11 x )}{2 sin ( 11 x )}

= \frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \cdot \frac{11 cos ( 11 x )}{2 sin ( 11 x )}

簡素化

\frac{1}{1 - ( sin ( 11 x ) ) ^{2}} \cdot \frac{11 cos ( 11 x )}{2 sin ( 11 x )} : \frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}

= \frac{11 cos ( 11 x )}{2 sin ( 11 x ) 1 - sin ( 11 x )}