derivative (3+csc(2t))^{-6}

解

導関数

(3 + csc (2 t))^{- 6}

\frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}

解答ステップ

\frac{d}{d t} ((3 + csc (2 t))^{- 6})

連鎖法則を適用:

- \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} \frac{d}{d t} (3 + csc (2 t))

= - \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} \frac{d}{d t} (3 + csc (2 t))

\frac{d}{d t} (3 + csc (2 t)) = - 2 cot (2 t) csc (2 t)

= - \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} (- 2 cot (2 t) csc (2 t))

簡素化

- \frac{6}{( 3 + csc ( 2 t ) ) ^{7}} (- 2 cot (2 t) csc (2 t)) : \frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}

= \frac{12 cot ( 2 t ) csc ( 2 t )}{( 3 + csc ( 2 t ) ) ^{7}}