Learning Outcomes
 Understand the derivative of an inverse function.
 Calculate derivatives of the standard inverse trigonometric functions.
Textbook
 Chapter 3.7 Derivatives of Inverse Functions
Textbook Assignment
 p. 306: 265, 267, 279283 all, 287
WeBWork Assignment
 DerivativesInverses
Exit problems of the session

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.
$\dfrac{d}{dx}(\sin^{1}x)=\dfrac{1}{\sqrt{1x^2}}$
$\dfrac{d}{dx}(\cos^{1}x)=\dfrac{1}{\sqrt{1x^2}}$
$\dfrac{d}{dx}(\tan^{1}x)=\dfrac{1}{1+x^2}$
$\dfrac{d}{dx}(\cot^{1}x)=\dfrac{1}{1+x^2}$
$\dfrac{d}{dx}(\sec^{1}x)=\dfrac{1}{x\sqrt{x^21}}$
$\dfrac{d}{dx}(\csc^{1}x)=\dfrac{1}{x\sqrt{x^21}}$
Videos and Practice Problems of Selected Topics
 $\rhd$ Derivatives of inverse functions from equation (5:03) Given $f(x) =\dfrac{1}{2}x^3+3x4$ and let $h$ be the inverse function of $f$. Notice that $f(2)=14$. Find $h'(14)$.
 $\rhd$ Derivatives of inverse sine function (4:55) Deriving the formula of inverse sine function, $\sin^{1}x$.
 $\rhd$ Derivatives of inverse cosine function (3:43) Deriving the formula of inverse cosine function, $\cos^{1}x$.
 $\rhd$ Derivatives of inverse tangent function (6:01) Deriving the formula of inverse tangent function, $\tan^{1}x$.
 * Practice: Derivatives of inverse trigonometric functions. (4 problems)