Math151PopSols

Math151PopSols - MATH 151 POP QUIZ: SOLUTIONS DERIVATIVES...

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MATH 151 POP QUIZ: SOLUTIONS DERIVATIVES (CHAPTERS 3, 7, and 8) Dx x x sin cos () = x x cos sin =- x x tan sec = 2 x x cot csc 2 x x x sec sec tan = x x x csc csc cot Take a look at each row: we are taking the derivatives of a pair of cofunctions. To get from the first column to the second column, you flip the sign of the result and take the cofunction of each factor. Evaluate the following: x x x 4 1 7 3 3 5 -++ Ê Ë Á ˆ ¯ ˜ D x is a linear operator: we can differentiate term-by-term, and constant factors “pop out.” Dxx x xx x D x n x x x x nn 47 43 1 3 50 12 1 3 5 31 3 5 22 3 6 1 3 6 =-- + = - - -- - () () / / / Power Rule: x 731 0 73 10 7 3 14 140 7 3 2 10 2 9 2 2 9 2 9 += + + =+ "Tail" from the Chain Rule 12 4 44 x x D x sec sec tan sec tan 4 4 4 [] =◊ = Tail = 4 4
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Dx D x xD x xx D x x x sin sin sin sin sin cos sin cos 4 4 3 3 3 3 33 43 3 3 3 12 3 3 () [] () () () () () = =◊ = = Tail 12 4 44 4 x x x D x x x x 3 23 2 3 tan tan tan tan sec ( ) È Î Í ˘ ˚ ˙ =+ by the Product Rule D x x xDx x D x x x x x sin sin sin cos sin 31 3 3 2 2 + = ◊- ¢ = +◊ - + + = +- + Ê Ë Á ˆ ¯ ˜ ()() = Lo D Hi Hi D Lo the square of what s below by the Quotient Rule 67 48 4 De e x = eD eeD blah e x blah blah x x 4 4 4 = = Tail=4 Think: 4 .
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This note was uploaded on 09/08/2011 for the course MATH 151 taught by Professor Bray during the Spring '07 term at Mesa CC.

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Math151PopSols - MATH 151 POP QUIZ: SOLUTIONS DERIVATIVES...

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