derivative of 6ln(sec(x+tan(x)))

解

\frac{d}{d x} (6 ln (sec (x) + tan (x)))

- \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}

解答ステップ

\frac{d}{d x} (6 ln (sec (x) + tan (x)))

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \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 )}

= 6 \cdot \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )})

簡素化

6 \cdot \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : - \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}

= - \frac{6}{( sec ( x ) + tan ( x ) ) ( - 1 + sin ( x ) )}