Differentiation of Inverse Trigonometric Functions

Each of the six basic trigonometric functions have corresponding inverse functions when appropriate restrictions are placed on the domain of the original functions. All the inverse trigonometric functions have derivatives, which are summarized as follows:

  

Example 1: Find f′( x) if f( x) = cos ⁻¹(5 x).

  

Example 2: Find y′ if .