derivative ln(4-2cos(x))

解

導関数

ln (4 - 2 cos (x))

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

解答ステップ

\frac{d}{d x} (ln (4 - 2 cos (x)))

連鎖法則を適用:

\frac{1}{4 - 2 cos ( x )} \frac{d}{d x} (4 - 2 cos (x))

= \frac{1}{4 - 2 cos ( x )} \frac{d}{d x} (4 - 2 cos (x))

\frac{d}{d x} (4 - 2 cos (x)) = 2 sin (x)

= \frac{1}{4 - 2 cos ( x )} \cdot 2 sin (x)

簡素化

\frac{1}{4 - 2 cos ( x )} \cdot 2 sin (x) : \frac{sin ( x )}{2 - cos ( x )}

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