derivative of (sec(x+tan(x))^{-3})

解

\frac{d}{d x} ((sec (x) + tan (x))^{- 3})

\frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}

解答ステップ

\frac{d}{d x} ((sec (x) + tan (x))^{- 3})

連鎖法則を適用:

- \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} \frac{d}{d x} (sec (x) + tan (x))

= - \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} \frac{d}{d x} (sec (x) + tan (x))

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

= - \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} (- \frac{1}{- 1 + sin ( x )})

簡素化

- \frac{3}{( sec ( x ) + tan ( x ) ) ^{4}} (- \frac{1}{- 1 + sin ( x )}) : \frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}

= \frac{3}{( sec ( x ) + tan ( x ) ) ^{4} ( - 1 + sin ( x ) )}