derivative of (1+cos(2x)/(1-cos(2x)))

解

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

- 2 csc^{2} (x) cot (x)

解答ステップ

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

簡素化

\frac{1 + cos ( 2 x )}{1 - cos ( 2 x )} : cot^{2} (x)

= \frac{d}{d x} (cot^{2} (x))

連鎖法則を適用:

2 cot (x) \frac{d}{d x} (cot (x))

= 2 cot (x) \frac{d}{d x} (cot (x))

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= 2 cot (x) (- csc^{2} (x))

簡素化

= - 2 csc^{2} (x) cot (x)