Calc03_8 - 3.8 Derivatives of Inverse Trig Functions Lewis...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
3.8 Derivatives of Inverse Trig Functions Lewis and Clark Caverns, Montana Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1993
Background image of page 1

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

View Full DocumentRight Arrow Icon
( 29 2 0 f x x x = We can find the inverse function as follows: 2 y x = Switch x and y . 2 x y = x y = y x = 2 y x = y x = 2 df x dx = At x = 2 : ( 29 2 2 2 4 f = = ( 29 2 2 2 4 df dx = ⋅ = 4 m = ( 29 2,4 ( 29 1 f x x - = ( 29 1 1 2 f x x - = 1 1 2 1 2 df x dx - - = 1 1 2 df dx x - = To find the derivative of the inverse function:
Background image of page 2
( 29 2 0 f x x x = 2 y x = y x = 2 df x dx = At x = 2 : ( 29 2 2 2 4 f = = ( 29 2 2 2 4 df dx = ⋅ = 4 m = ( 29 2,4 ( 29 1 f x x - = 1 1 2 df dx x - = ( 29 1 1 1 1 4 2 2 4 2 4 df dx - = = = At x = 4 : ( 29 1 4 4 2 f - = = ( 29 4,2 1 4 m = Slopes are reciprocals.
Background image of page 3

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

View Full DocumentRight Arrow Icon
y x = y x = 4 m = ( 29 2,4 ( 29 4,2 1 4 m = Slopes are reciprocals. Because x and y are reversed to find the reciprocal function, the following pattern always holds: Derivative Formula for Inverses: df dx df dx x f a x a - = = = 1 1 ( ) evaluated at
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.

Page1 / 9

Calc03_8 - 3.8 Derivatives of Inverse Trig Functions Lewis...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online