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

解

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

2 tan (x) sec^{2} (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 )} : tan^{2} (x)

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

連鎖法則を適用:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= 2 tan (x) sec^{2} (x)