derivative of arccsc(-9x^2)

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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