Problem Set 08s

Problem Set 08s - Hung Nguyen Problem Set 08 Solution 3.6...

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Hung Nguyen Problem Set 08 Solution GE 207C 3.6 Derivatives of Logarithmic Functions 1 1. Find the derivative dy/dx a. f x ( ) = 4ln x + x 2 6 ( ) , x > 3 ( ) b. G u ( ) = ln 6 u + 5 6 u 5 c. ( ) x x f 2 sin ln ) ( = Solution: ( ) ( )( ) x x x x x x x f x x f 2 2 2 sin cos sin 2 cos sin 2 sin 1 ) ( ' sin ) ( = = = x x f cot 2 ) ( ' = d. f ( x ) = log 5 xe x ( ) Solution: f (' x ) = 1 xe x ln 5 d dx xe x ( ) = 1 xe x ln 5 e x + xe x ( ) = e x + xe x xe x ln 5 5 ln 1 ) ( ' x x x f + = e. ( ) x x y 2 4 sin = Solution: ( ) ( ) [ ] x x x x x x x y cos sin 2 sin 4 sin 1 ' 4 2 3 2 4 + = ( ) ( ) x x x x x x x y 2 4 4 2 3 sin cos sin 2 sin 4 ' + = ( ) x x x x x x x y cot 2 4 sin cos 2 sin 4 ' + = + = f. ( ) [ ] 2 1 x e y + = Solution: ( ) [ ] ( ) x x x x e e e y e y Ο Π Ξ Μ Ν Λ + + = + = 1 1 1 2 ' 1 2 ( ) x x x e e e y + + = 1 1 ln 2 ' 2. Use logarithmic differentiation to find the derivative of the function a. x x y cos = Solution: ( ) ( ) y x x x x y x x x x x x x x y y x x y x y x y x x Υ Φ Τ ΢ Σ Ρ = = + = = = = ln sin cos ' ln sin cos 1 cos ln sin ' 1 ln cos ln ln ln cos cos Υ Φ Τ ΢ Σ Ρ = x x x x x x y x ln sin cos ' cos b.
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Problem Set 08s - Hung Nguyen Problem Set 08 Solution 3.6...

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