derivative of arccsc(-5x^2)

解答

\frac{d}{d x} (arccsc (- 5 x^{2}))

\frac{2}{x 25 x ^{4} - 1}

求解步骤

\frac{d}{d x} (arccsc (- 5 x^{2}))

使用连锁律:

- \frac{1}{( - 5 x ^{2} ) ^{2} ( - 5 x ^{2} ) ^{2} - 1} \frac{d}{d x} (- 5 x^{2})

= - \frac{1}{( - 5 x ^{2} ) ^{2} ( - 5 x ^{2} ) ^{2} - 1} \frac{d}{d x} (- 5 x^{2})

\frac{d}{d x} (- 5 x^{2}) = - 10 x

= - \frac{1}{( - 5 x ^{2} ) ^{2} ( - 5 x ^{2} ) ^{2} - 1} (- 10 x)

化简

- \frac{1}{( - 5 x ^{2} ) ^{2} ( - 5 x ^{2} ) ^{2} - 1} (- 10 x) : \frac{2}{x 25 x ^{4} - 1}

= \frac{2}{x 25 x ^{4} - 1}

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