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Derivatives · Inverse Trigonometric

Derivative of arccsc(x)

ddx[arccsc x]=−1∣x∣x2−1\frac{d}{dx}[\text{arccsc}\, x] = -\frac{1}{|x|\sqrt{x^2 - 1}}

The derivative of the inverse cosecant function. Note the negative sign, mirroring the arcsec derivative.

Conditions. |x| > 1.
  • 2 worked examples
  • 24 in Derivatives

Worked examples

Find d/dx[arccsc(3x)].
  1. Chain rule: -1/(|3x|√((3x)²-1)) · 3 = -3/(|3x|√(9x²-1)) = -1/(|x|√(9x²-1))

Answer: -1/(|x|√(9x² - 1))

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Find d/dx[arccsc(x)] at x = 2.

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Common questions

What is the Derivative of arccsc(x)?

The derivative of the inverse cosecant function. Note the negative sign, mirroring the arcsec derivative. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of arccsc(x) apply?

The Derivative of arccsc(x) holds under this condition: |x| > 1.

How do you use the Derivative of arccsc(x)?

Worked example. Find d/dx[arccsc(3x)]. Chain rule: -1/(|3x|√((3x)²-1)) · 3 = -3/(|3x|√(9x²-1)) = -1/(|x|√(9x²-1)). Answer: -1/(|x|√(9x² - 1)).

Practice

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