derivative arccsc(-9t^2)

解

導関数

arccsc (- 9 t^{2})

\frac{2 t}{t ^{4} 81 t ^{4} - 1}

解答ステップ

\frac{d}{d t} (arccsc (- 9 t^{2}))

連鎖法則を適用:

- \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} \frac{d}{d t} (- 9 t^{2})

= - \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} \frac{d}{d t} (- 9 t^{2})

\frac{d}{d t} (- 9 t^{2}) = - 18 t

= - \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} (- 18 t)

簡素化

- \frac{1}{( - 9 t ^{2} ) ^{2} ( - 9 t ^{2} ) ^{2} - 1} (- 18 t) : \frac{2 t}{t ^{4} 81 t ^{4} - 1}

= \frac{2 t}{t ^{4} 81 t ^{4} - 1}