Whitman College: David Guichard's "Calculus, Chapter 4: Transcendental Functions, Section 4.9: Inverse Trigonometric Functions"

Read Section 4.9 (pages 91-94). In this reading, implicit differentiation and the Pythagorean identity are used to compute the derivatives of inverse trigonometric functions. You should notice that the same techniques can be used to find derivatives of other inverse functions as well.