Learning Outcomes

  1. Understand the derivative of an inverse function.
  2. Calculate derivatives of the standard inverse trigonometric functions.


  • Chapter 3.7   Derivatives of Inverse Functions  

Textbook Assignment

  • p. 306:    265, 267, 279-283 all, 287

WeBWork Assignment

  • Derivatives-Inverses

Exit problems of the session 

  1. Find the derivative of the following functions:

    (a).  $y=\cos^{-1}(\sqrt{x})$    (b).   $y=x\tan^{-1}(3x)$   (c).  $y=(1+\sin^{-1}x)^3$


Key Concepts

  • Differentiation formulas for the inverse trigonometric functions.








Videos and Practice Problems of Selected Topics

  1. $\rhd$ Derivatives of inverse functions from equation (5:03) Given $f(x) =\dfrac{1}{2}x^3+3x-4$ and let $h$ be the inverse function of $f$.  Notice that $f(-2)=-14$.  Find $h'(-14)$.
  2. $\rhd$ Derivatives of inverse sine function (4:55) Deriving the formula of inverse sine function, $\sin^{-1}x$. 
  3. $\rhd$ Derivatives of inverse cosine function (3:43) Deriving the formula of inverse cosine function, $\cos^{-1}x$.
  4. $\rhd$ Derivatives of inverse tangent function (6:01) Deriving the formula of inverse tangent function, $\tan^{-1}x$.
  5. * Practice: Derivatives of inverse trigonometric functions. (4 problems)