131f11x2ans - Math 131 Exam 2 Solutions October 27, 2011 In...

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Unformatted text preview: Math 131 Exam 2 Solutions October 27, 2011 In #15, intermediate steps need not be shown Optional simplified forms are shown inside { braces } 1. [11%] d dx ( 3 x 4 / 3 + e ) = 3 4 3 x 1 / 3 + 0 n = 4 x 1 / 3 o (could write x 1 / 3 as 3 x ) 2. [11%] d dx 1 + tan x x 2 = x 2 d dx (1 + tan x )- (1 + tan x ) d dx x 2 ( x 2 ) 2 = x 2 sec 2 x- (1 + tan x )(2 x ) ( x 2 ) 2 = x 2 sec 2 x- 2 x (1 + tan x ) x 4 = x sec 2 x- 2(1 + tan x ) x 3 3. [11%] d dx x 3 e 1 /x = x 3 d dx ( e 1 /x ) + e 1 /x d dx ( x 3 ) = x 3 e 1 /x d dx (1 /x ) + e 1 /x 3 x 2 = x 3 e 1 /x- 1 x 2 + e 1 /x 3 x 2 n = (3 x 2- x ) e 1 /x o 4. [11%] d dx ln(arcsin x ) = 1 arcsin x d dx (arcsin x ) = 1 arcsin x 1 1- x 2 = 1 1- x 2 arcsin x 5. [11%] Method 1Product Rule: d dx e- x/ 8 cos3 x = e- x/ 8 d dx (cos3 x ) + (cos3 x ) d dx e- x/ 8 = e- x/ 8- sin3 x d dx (3 x ) + (cos3 x ) e- x/ 8 d dx- x 8 = e- x/ 8 (- sin3 x )(3) + (cos3 x ) e- x/ 8 (- 1 8 ) =- e- x/ 8 3 sin3 x + 1 8 cos3 x Method 2Quotient Rule:...
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131f11x2ans - Math 131 Exam 2 Solutions October 27, 2011 In...

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