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Inverse Trig Derivatives

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Inverse trig functions (arcsin, arccos, arctan) have derivatives that involve square roots. These are worth memorizing for integration later.

Inverse Trig Derivatives
Inverse Trig with Chain Rule
Medium
Find d/dx[arctan(2x)]
1
Apply chain rule
= 1/(1+(2x)^2) * 2 = 2/(1+4x^2)
Answer: 2/(1+4x^2)

Practice

1. d/dx[arcsin(x)] = ?
1/sqrt(1-x^2)
-1/sqrt(1-x^2)
1/(1+x^2)
sqrt(1-x^2)
Key Takeaways

  • arcsin and arccos have sqrt(1-x^2) in denominator

  • arctan has 1+x^2 in denominator

  • arccos is negative of arcsin

  • These formulas appear often in integration