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Derivatives · Inverse Trigonometric

Derivative of arcsec(x)

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

The derivative of the inverse secant function.

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

Worked examples

Find d/dx[arcsec(2x)].
  1. Chain rule: 1/(|2x|√((2x)²-1)) · 2 = 2/(|2x|√(4x²-1)) = 1/(|x|√(4x²-1))

Answer: 1/(|x|√(4x² - 1))

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

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Common questions

What is the Derivative of arcsec(x)?

The derivative of the inverse secant function. It is one of the derivatives formulas in the CalcRef reference.

When does the Derivative of arcsec(x) apply?

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

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

Worked example. Find d/dx[arcsec(2x)]. Chain rule: 1/(|2x|√((2x)²-1)) · 2 = 2/(|2x|√(4x²-1)) = 1/(|x|√(4x²-1)). Answer: 1/(|x|√(4x² - 1)).

Practice

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