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Finding Derivatives

Finding Derivatives. Problem is taken from Worksheet 9, #3. By: Rachel Atmadja, 2002. Finding Derivatives. y = ln x - 4x. 4. Finding Derivatives. y = ln x - 4x. 4. Remember: y = ln y’= ‘. 1. Finding Derivatives. y = ln x - 4x y = ln (x - 4x).

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Finding Derivatives

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  1. Finding Derivatives Problem is taken from Worksheet 9, #3 By: Rachel Atmadja, 2002

  2. Finding Derivatives y = ln x - 4x 4

  3. Finding Derivatives y = ln x - 4x 4 Remember: y = ln y’= ‘ 1

  4. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4

  5. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 -½ = ½ (x - 4x) (4x - 4) 4 3

  6. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 -½ = ½ (x - 4x) (4x - 4) 4 3 4 (x - 1) 2 x - 4x 3 = 4

  7. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 -½ = ½ (x - 4x) (4x - 4) 4 3 4 (x - 1) 2 x - 4x 3 = 4 Remember: y = ln y’= ‘ 1

  8. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 -½ = ½ (x - 4x) (4x - 4) 4 3 4 (x - 1) 2 x - 4x 3 = 1 4 4 (x - 1) 2 x - 4x 3 1 x - 4x 4 4

  9. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 -½ = ½ (x - 4x) (4x - 4) 4 3 4 (x - 1) 2 x - 4x 3 = 4 2 4 (x - 1) 2 x - 4x 3 1 x - 4x 2 (x - 1) x - 4x 3 = 1 4 4 4

  10. Finding Derivatives y = ln x - 4x y = ln (x - 4x) 4 ½ 4 2 ( x - 1) x (x - 4) 3 -½ = ½ (x - 4x) (4x - 4) 4 3 3 4 (x - 1) 2 x - 4x 3 = 4 2 4 (x - 1) 2 x - 4x 3 1 x - 4x 2 (x - 1) x - 4x 3 Don’t forget to factor! = 1 4 4 4

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