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Unformatted text preview: Page 46 Determine the derivative of the inverse tangent function: Two new formulas: Arctan x ( ) ′ = tan1 x ( ) ′ = Arctan u ( ) ′ = tan1 u ( ) ′ = Example 4 A particle moves along a line so that its position at any time t ≥ 0 is s t ( ) = tan1 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 = tan1 x at the point 1,π 4 . There are other inverse trigonometric functions . Here are their derivative formulas: Calculus Section 3.6 Page47 cos1 u ( ) ′ = cot1 u ( ) ′ = sec1 u ( ) ′ = csc1 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 = sin1 x1x 2 , determine ′ y ....
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 Spring '10
 John
 Calculus, Derivative, Inverse Functions, Inverse function, Inverse trigonometric functions, inverse trigonometric function, Calculus Section, Arctangent Function

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