derivative of ln(sec(x+tan(x)))

解

\frac{d}{d x} (ln (sec (x) + tan (x)))

sec (x)

解答ステップ

\frac{d}{d x} (ln (sec (x) + tan (x)))

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : sec (x)

= sec (x)