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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.
  • 2 worked examples
  • 24 in Derivatives

Worked examples

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

Answer: 2/√(1 - 4x²)

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Find d/dx[arcsin(x/3)].

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Related formulas

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

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Common questions

What is the Derivative of arcsin(x)?

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

When does the Derivative of arcsin(x) apply?

The Derivative of arcsin(x) holds under this condition: -1 < x < 1.

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

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

Practice

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