derivative of ln(ln(sec(x)))

解

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

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

解答ステップ

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

連鎖法則を適用:

\frac{1}{ln ( sec ( x ) )} \frac{d}{d x} (ln (sec (x)))

= \frac{1}{ln ( sec ( x ) )} \frac{d}{d x} (ln (sec (x)))

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

= \frac{1}{ln ( sec ( x ) )} tan (x)

簡素化

\frac{1}{ln ( sec ( x ) )} tan (x) : \frac{tan ( x )}{ln ( sec ( x ) )}

= \frac{tan ( x )}{ln ( sec ( x ) )}