derivative (1+cos(5t))^{-4}

解

導関数

(1 + cos (5 t))^{- 4}

\frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}

解答ステップ

\frac{d}{d t} ((1 + cos (5 t))^{- 4})

連鎖法則を適用:

- \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} \frac{d}{d t} (1 + cos (5 t))

= - \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} \frac{d}{d t} (1 + cos (5 t))

\frac{d}{d t} (1 + cos (5 t)) = - 5 sin (5 t)

= - \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} (- 5 sin (5 t))

簡素化

- \frac{4}{( 1 + cos ( 5 t ) ) ^{5}} (- 5 sin (5 t)) : \frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}

= \frac{20 sin ( 5 t )}{( 1 + cos ( 5 t ) ) ^{5}}