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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 - π 2 , π 2 Ατξ=1, ψ= π 2 Domain [-1,1] Range 0, π [ ] Ατξ=1, ψ=0 Domain All Reals; Range - π 2 , π 2 ÷ Ατξ=1, ψ= π 4 Domain -∞,1 ( ] ∪ 1,∞ [ 29 Ρανγε 0, π 2 ÷ ∪ π 2 ,π Ατξ=1, ψ= 0 Domain All Reals; Range All Reals; At x=1, y = 1 f-1 ξ ( 29 = ξ + 8 3 f-1 ξ ( 29 = ξ 3- 5 f-1 ξ ( 29 = 8 ξ f-1 ξ ( 29 = 2 3 - ξ f-1 ξ ( 29 = 3ταν ξ, - π 2 < ξ < π 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 = ³ 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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Calc03_8 - 3.8 Derivatives of Inverse Trig Functions...

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