d/(dt)(ln(sec(t)))

解

\frac{d}{d t} (ln (sec (t)))

tan (t)

解答ステップ

\frac{d}{d t} (ln (sec (t)))

連鎖法則を適用:

\frac{1}{sec ( t )} \frac{d}{d t} (sec (t))

= \frac{1}{sec ( t )} \frac{d}{d t} (sec (t))

\frac{d}{d t} (sec (t)) = sec (t) tan (t)

= \frac{1}{sec ( t )} sec (t) tan (t)

簡素化

\frac{1}{sec ( t )} sec (t) tan (t) : tan (t)

= tan (t)