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Derivatives · Inverse Trigonometric

Derivative of arcsin(x)

ddx[arcsin⁡x]=11−x2\frac{d}{dx}[\arcsin x] = \frac{1}{\sqrt{1 - x^2}}

The derivative of the inverse sine function.

Conditions. -1 < x < 1.

Worked examples

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

Answer: 2/√(1 - 4x²)

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

Answer: 1/√(9 - x²)

Related formulas

Derivative of arccos(x)Derivative of arctan(x)

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