1.5 Class Notes - HWK #3. Due Tues 2/13, Wed 2/14 Solutions...

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HWK #3. Due Tues 2/13, Wed 2/14 Solutions will be available 2/15 4.3: 22, 28, 36, 46 4.4: 2, 8, 18, 38b Not HWK. 4.5: 1, 7, 9, 11 Prelim 1: Tues 2/20 covers 3.3-4.5 Rule 1: (x p ) = px p-1 Rule 2: (cf) = cf Rule 3. (f+g) = f + g Rule 4. (fg) = f g + f g Rule 5. (1/g) = - g / g 2 Rule 6. (f/g) = (f g - f g ) / g 2 Rule 7. (f(g)) = f (g) g () ( ) ( ( ( )) ( ( )) ' (() ) ' )( ) gx h gx gx h fgx h fgx h h fgx g x x g +− = + + Rule 7. (f(g)) = f (g) g 53 2 Find the derivative of (2 ) xx + Rule 7. (f(g)) = f (g) g 2 25 3 42 97 5 ) ( ) ( ) 2 '( ) 2 '( ) 5 6 Ans (2 4 )(5 6 ) 10 (12 20) 24 fg g g x fg g g xxx x + == + + =+ + + + A second solution 22 2 2 1 086 975 2 ) 44 10 32 24 ab a a bb x += + + + + =++
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Rule 7. (f(g)) = f (g) g 3 Find the derivative of 2 xx + Rule 7. (f(g)) = f (g) g 3 1/ 2 3 2 31 / 2 2 2 ( ) 2 '( ) (1/ 2) 3 2 Ans (1/ 2)( 2 ) (3 2) fg g g x fg g gx x x + == + + =+ + Gottfreid Willhelm Leibniz 1646-1716 df df dg dx dg dx =⋅ Economics word problem Demand D(p) = 9 - .01 p 2 Revenue
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1.5 Class Notes - HWK #3. Due Tues 2/13, Wed 2/14 Solutions...

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