What is the derivative of arccsc(-x^2) ?

The derivative of arccsc(-x^2) is 2/(xsqrt(x^4-1))

What is the first derivative of arccsc(-x^2) ?

The first derivative of arccsc(-x^2) is 2/(xsqrt(x^4-1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of arccsc(-x^2) ?
The derivative of arccsc(-x^2) is 2/(xsqrt(x^4-1))
What is the first derivative of arccsc(-x^2) ?
The first derivative of arccsc(-x^2) is 2/(xsqrt(x^4-1))