03Techniques of DifferentiationII

03Techniques of DifferentiationII - g f F = and 2 x g x g x...

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T ECHNIQUES OF D IFFERENTIATION – P RODUCT AND Q UOTIENT R ULES Leibniz discovered the correct formula for the derivative of a product ) ( fg . Product Rule If f and g are both differentiable, then so is fg and g f g f fg + = ) ( , or Proof is available upon request. Ex . Differentiate ) 3 )( 5 2 ( 2 3 x x x y - + = using the product rule. Ex . Find the slope of the tangent to the graph of ) 1 2 )( 2 3 ( ) ( 3 2 - + = x x x f at (1, 5). Extension of the Product Rule [ ] ) ( ) ( ) ( ) ( ) ( ) ( x f dx d x g x g dx d x f x g x f dx d + = [ ] ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( x h dx d x g x f x f dx d x h x g x g dx d x h x f x h x g x f dx d + + =

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Ex . Find [ ] dt t t t d ) 5 )( 7 3 )( 3 ( 3 4 2 + - + . Quotient Rule If f and g are both differentiable, then so is
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Unformatted text preview: g f F = and [ ] 2 ) ( ) ( ) ( ) ( ) ( ) ( x g x g x f x f x g x F ′-′ = ′ , 2 g g f g f g f ′-′ = ′ . Look for the product and quotient rules on the formula sheet. Ex . Differentiate 6 2 5 2 +-+ = x x x y . Ex . Differentiate 3 2-= x x y . Assign: p.195 ex.6; p.198 #15, 16, 19, 21, 25-28, Unit 2 Assignment...
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This note was uploaded on 07/12/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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03Techniques of DifferentiationII - g f F = and 2 x g x g x...

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