{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Copy_of_3.8_notes - Page 46 Determine the derivative of the...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Calculus Section 3.6 Page 44 3.8 Derivatives of Inverse Functions and Inverse Trigonometric Functions Example 1 Let f x ( ) = x 5 + 2 x - 1 . a) Since the point 1,2 ( ) is on the graph of f , why does it follow that the point 2,1 ( ) is on the graph of f - 1 ? b) Determine df - 1 dx 2 ( ) c) Develop a shortcut formula for f - 1 x ( ) ( ) f - 1 x ( ) ( ) = Example 2 Let f x ( ) = x 3 + x 2 + 1 a) Find f 1 ( ) and f 1 ( ) b) Find f - 1 3 ( ) and f - 1 ( ) 3 ( ) Derivative of the Arcsine Function Consider the function y = sin x What is the inverse of this function: Solve for y :
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Calculus Section 3.6 Page45 Use your graphing calculator to graph this inverse trigonometric function: What is the domain and range? Determine the derivative of the inverse sine function: Two new formulas: Arcsin x ( ) = sin - 1 x ( ) = Arcsin u ( ) = sin - 1 u ( ) = Example 3 Determine: d dx sin - 1 x 2 ( ) Derivative of the Arctangent Function Consider the function y = tan x What is the inverse of this function: Solve for y : Use your graphing calculator to graph this inverse trigonometric function: What is the domain and range?
Image of page 2
Calculus Section 3.6
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Page 46 Determine the derivative of the inverse tangent function: Two new formulas: Arctan x ( ) ′ = tan-1 x ( ) ′ = Arctan u ( ) ′ = tan-1 u ( ) ′ = Example 4 A particle moves along a line so that its position at any time t ≥ 0 is s t ( ) = tan-1 t . What is the velocity of the particle when t = 16? Example 5 a) Find an equation for the line tangent to the graph of y = tan x at the point -π 4 ,-1 . b) Find an equation for the line tangent to the graph of y = tan-1 x at the point -1,-π 4 . There are other inverse trigonometric functions . Here are their derivative formulas: Calculus Section 3.6 Page47 cos-1 u ( ) ′ = cot-1 u ( ) ′ = sec-1 u ( ) ′ = csc-1 u ( ) ′ = Example 5 Find dy dx for y = sin 1 x Assignment II–8 Pages 162 – 163 #1, 2, 3, 4, 6, 10, 11, 13, 16, 19 Additional Question: Given y = sin-1 x-1-x 2 , determine ′ y ....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern