AP Calculus AB and BC glossary

Inverse trigonometric derivatives

The derivatives of the inverse trigonometric functions are algebraic, not trigonometric. Arcsin x has derivative one over the square root of one minus x squared, and arctan x has derivative one over one plus x squared. Arccos and arccot are the negatives of their partners.

ddxarcsin⁡x=11−x2,ddxarctan⁡x=11+x2\frac{d}{dx}\arcsin x = \frac{1}{\sqrt{1 - x^{2}}}, \quad \frac{d}{dx}\arctan x = \frac{1}{1 + x^{2}}

Read backwards these are antiderivative facts, and that is where they earn most of their exam marks. Recognizing one over one plus x squared as arctan is a Unit 6 skill that starts here in Topic 3.4.

The mistake

Missing the minus sign on the co-functions. Arccos and arccot have exactly the negatives of the arcsin and arctan derivatives.

Appears in: Unit 3: Chain Rule, Implicit, and Inverses