2.3 Differentiation Formulas

2.3 Differentiation Formulas - The Product Rule v The...

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Differentiation Formulas Section 2.3
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The Constant Rule v The derivative of a constant function is 0. That is, if c is a real number, then [ ] 0 = c dx d
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The Power Rule v If n is a positive integer or if n is a negative integer and x 0, then [ ] 1 - = n n nx x dx d
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v In the Power Rule, the case for which n = 1 is best thought of as a separate differentiation rule. That is, [ ] 1 = x dx d
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The Constant Multiple Rule v If f is a differentiable function and c is a real #, then cf is also differentiable and [ ] ) ( ' ) ( x cf x cf dx d =
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The Sum and Difference Rules v The derivative of the sum (or difference) of two differentiable functions is differentiable and is the sum (or difference) of their derivatives. [ ] ) ( ' ) ( ' ) ( ) ( x g x f x g x f dx d ± = ±
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Unformatted text preview: The Product Rule v The product of two differentiable functions u and v is differentiable, and ( 29 d dv du uv u v dx dx dx = + The Quotient Rule v At a point where v o, the quotient of two differentiable functions is differentiable, and u y v = 2 du dv v u d u dx dx dx v v- = Theorem 2.6 Derivatives of Sine and Cosine Functions [ ] x x dx d cos sin = [ ] x x dx d sin cos-= Joke Time v Why was Cinderella such a bad baseball player? v She ran away from the ball! v What did Snow White say when the snapshots shed ordered didnt arrive? v Someday my prints will come!...
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2.3 Differentiation Formulas - The Product Rule v The...

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