CalcRef

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.

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))

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

Answer: -√3/6 ≈ -0.2887

Practice this and 135 more formulas in the CalcRef workspace — quizzes, reference tables, a 16-category unit converter, and an expression evaluator.