derivative sqrt(1+sec(2x))

解

導関数

1 + sec (2 x)

\frac{sec ( 2 x ) tan ( 2 x )}{1 + sec ( 2 x )}

解答ステップ

\frac{d}{d x} (1 + sec (2 x))

連鎖法則を適用:

\frac{1}{2 1 + sec ( 2 x )} \frac{d}{d x} (1 + sec (2 x))

= \frac{1}{2 1 + sec ( 2 x )} \frac{d}{d x} (1 + sec (2 x))

\frac{d}{d x} (1 + sec (2 x)) = 2 sec (2 x) tan (2 x)

= \frac{1}{2 1 + sec ( 2 x )} \cdot 2 sec (2 x) tan (2 x)

簡素化

\frac{1}{2 1 + sec ( 2 x )} \cdot 2 sec (2 x) tan (2 x) : \frac{sec ( 2 x ) tan ( 2 x )}{1 + sec ( 2 x )}

= \frac{sec ( 2 x ) tan ( 2 x )}{1 + sec ( 2 x )}