Calc03_8 - 3.8 Derivatives of Inverse Trig Functions...

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Unformatted text preview: 3.8 Derivatives of Inverse Trig Functions Inverse Sine on the Complex Plane Domain [-1,1] Range - 2 , 2 =1, = 2 Domain [-1,1] Range 0, [ ] =1, =0 Domain All Reals; Range - 2 , 2 =1, = 4 Domain -,1 ( ] 1, [ 29 0, 2 2 , =1, = 0 Domain All Reals; Range All Reals; At x=1, y = 1 f-1 ( 29 = + 8 3 f-1 ( 29 = 3- 5 f-1 ( 29 = 8 f-1 ( 29 = 2 3 - f-1 ( 29 = 3 , - 2 < < 2 8 6 4 2 8 6 4 2 x y x y 8 6 4 2 8 6 4 2 x y x y 8 6 4 2 8 6 4 2 x y x y ( 29 2 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: 8 6 4...
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This note was uploaded on 02/16/2012 for the course CALCULUS 0064 taught by Professor Waldron during the Fall '10 term at Broward College.

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Calc03_8 - 3.8 Derivatives of Inverse Trig Functions...

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