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Derivatives of inverse trigonometric functions (d/dx(sin⁻¹x)=1/√(1−x²),d/dx(cos⁻¹x)=−1/√(1−x²),d/dx(tan⁻¹x)=1/(1+x²))

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d/dx(sin⁻¹x)=1/√(1−x²), d/dx(cos⁻¹x)=−1/√(1−x²), d/dx(tan⁻¹x)=1/(1+x²), d/dx(cot⁻¹x)=−1/(1+x²), d/dx(sec⁻¹x)=1/(|x|√(x²−1)), d/dx(csc⁻¹x)=−1/(|x|√(x²−1))

What each symbol means

SymbolWhat it stands for
xMust be in the domain of each inverse trig function

When to use this

sin⁻¹x, cos⁻¹x: |x| < 1; tan⁻¹x, cot⁻¹x: all real x; sec⁻¹x, csc⁻¹x: |x| > 1.