\log

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

3.26 Derivative of inverse cosine

Derivatives of inverse trigonometric functions unexpectedly produce algebraic functions.

Example

The derivative of the inverse cosine function is

{{d}\over{dx}}\cos^{-1}x={{-1}\over{\sqrt{1-x^{2}}}}\qquad(-1<x<1).

Solution. Let $y=\cos^{-1}x$ so that $x=\cos y$ . By the inverse function rule