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3 2-3 4 The 3.2-3.3 Derivative - Haas_ppt [Compatibility Mode]

3 2-3 4 The 3.2-3.3 Derivative - Haas_ppt [Compatibility Mode]

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Calculus I Note that you will need to write in several of the equations. I couldn’t get them to print properly. The Derivative 1 1 The Derivative Calculus I 2 Differentiation Rules n The Constant Rule If c is a real number then n The Power Rule If n is a real number, then [ ] 0 = c dx d [ ] 1 - = n n nx x dx d 3 More Differentiation Rules n The Constant Multiple Rule n The Sum and Difference Rules n The Natural Exponential Function [ ] ) ( ) ( ) ( ) ( x g x f x g x f dx d ± = ± [ ] ) ( ) ( x f c x cf dx d = [ ] x x e e dx d = 4 The Product Rule In words: The first times the derivative of the second plus the second times the derivative of the first. [ ] ) ( ) ( ) ( ) ( ) ( ) ( x f x g x g x f x g x f dx d + = 5 WARNING The derivative of a product is NOT the product of the derivatives! NO partial credit if you perform this no-no! 6 The Quotient Rule In words: The bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared. [ ] 0 ) ( , ) ( ) ( ' ) ( ) ( ' ) ( ) ( ) ( 2

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3 2-3 4 The 3.2-3.3 Derivative - Haas_ppt [Compatibility Mode]

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