Learning Activity 6-1

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Palmetto High School *

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123

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Mathematics

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Nov 24, 2024

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pdf

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MAC 2311 Learning Activity #6 Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions Name: Group #: 1. Prove the derivative of f ( x ) = tan x by using derivative rules. Use derivative rules to find the derivatives of the following functions. Simplify by combining like terms and canceling common factors. 2. f ( t ) = (5 + t 5 ) 5 5 √ t + 5 t 3. r ( θ ) = sec θ 1 + sec θ Page 1 of 3

MAC 2311 Learning Activity #6 Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions 4. Find an equation of the line tangent to the function g ( x ) = 2 x cos x at x = 3 π 2 . 5. Suppose there exists a function, f ( x ), such that f (1) = 4 and f 0 (1) = 5. Let h ( x ) = f ( x ) x + 1 . Find the equation of the tangent line to h ( x ) at x = 1. 6. Find the third derivative of f ( t ) = 3 t 3 - 2 t 2 Page 2 of 3

MAC 2311 Learning Activity #6 Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions 7. Find the 42 nd and 55 th derivative of f ( x ) = sin x . 8. Use this table to find the following: x 2 3 4 5 f ( x ) 2 3 4 3 g ( x ) 7 3 -1 2 f 0 ( x ) 5 7 -1 -2 g 0 ( x ) 3 -2 1 8 (a) d dx - 2 f ( x ) x =4 (b) d dx x 2 f ( x ) x =5 (c) Find the equation of the tangent line to y = g ( x ) f ( x ) at x = 3. Page 3 of 3

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Learning Activity 6-1

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