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Inverse Trig Derivatives

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