CalcRef

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.

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))

Find d/dx[arcsec(x)] at x = 2.
  1. 1/(|2|√(4-1)) = 1/(2√3) = √3/6

Answer: √3/6 ≈ 0.2887

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