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**Unformatted text preview: **Calculus Section 3.6 Page35 3.6 More on Chain Rule Formulas for Derivatives of Composite Functions: d dx u n ( ) = d dx sin u ( )= d dx cos u ( )= d dx tan u ( )= d dx cot u ( )= d dx sec u ( )= d dx csc u ( ) = Example 1 An object moves along the x-axis so that its position at any time t ≥ 0 is given by x t ( )= cos t 2 + 1 ( ) . Find the velocity of the object as a function of t . Example 2 a) Find the slope of the line tangent to the curve y = sin 5 x at the point where x = π 3 . b) Show that the slope of every line tangent to the curve y = 1 1- 2 x ( ) 3 is positive. Example 3 Going in, in, in Find the derivative of each function: a) y = tan 5- sin2 x ( ) Calculus Section 3.6 Page 36 b) y = 1 + cos 3 5 x ( ) 2 Background discussion about composite functions and function notation Example 4 Given f x ( ) = sin x and g x ( ) = x 3 , determine a) f o g = b) g o f = Example 5 Given f x ( ) = 2 + x 7 + x 3 and g x ( ) = 3- x , determine a) f o g ( ) ( ) = b) g o f ( ) ( ) = Calculus Section 3.6 Calculus Section 3....

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