derivative sqrt(6-5cos(2x))

解

導関数

6 - 5 cos (2 x)

\frac{5 sin ( 2 x )}{6 - 5 cos ( 2 x )}

解答ステップ

\frac{d}{d x} (6 - 5 cos (2 x))

連鎖法則を適用:

\frac{1}{2 6 - 5 cos ( 2 x )} \frac{d}{d x} (6 - 5 cos (2 x))

= \frac{1}{2 6 - 5 cos ( 2 x )} \frac{d}{d x} (6 - 5 cos (2 x))

\frac{d}{d x} (6 - 5 cos (2 x)) = 10 sin (2 x)

= \frac{1}{2 6 - 5 cos ( 2 x )} \cdot 10 sin (2 x)

簡素化

\frac{1}{2 6 - 5 cos ( 2 x )} \cdot 10 sin (2 x) : \frac{5 sin ( 2 x )}{6 - 5 cos ( 2 x )}

= \frac{5 sin ( 2 x )}{6 - 5 cos ( 2 x )}