# math9 - Math 2144 Exam II Oct 28 2010 Name Score Please...

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Math 2144, Exam II, Oct. 28, 2010 Name: Score: Please read the instructions on each problem carefully, and indicate answers as directed. Show details in your work. If you simply give a solution without steps of how you derive this solution, you may not get credit for it. The total is 50 points 1. (5 points) If f ( t ) = 4 t t 2 +6 , find f ( t ) . Solution f ( t ) = (4 t ) ( t 2 + 6) - (4 t )( t 2 + 6) ( t 2 + 6) 2 = (4)( t 2 + 6) - (4 t )(2 t ) ( t 2 + 6) 2 = - 4 t 2 + 24 ( t 2 + 6) 2 1

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2. (6 points) Use implicit differentiation to compute dy dx e y = cos( x + y ) Solution By taking derivative of both sides with respect to x , we have de y dx = d cos( x + y ) dx e y dy dx = - sin( x + y ) p 1 + dy dx P e y dy dx = - sin( x + y ) - sin( x + y ) dy dx e y dy dx + sin( x + y ) dy dx = - sin( x + y ) ( e y + sin( x + y )) dy dx = - sin( x + y ) dy dx = - sin( x + y ) e y + sin( x + y ) 2
3. (6 points) Use logarithmic differentiation to compute dy dx y = ( x ) x Solution First, take logarithm of both sides of the equation, we have ln y = ln ( x ) x = x ln x = x ln x 1 / 2 = x 2 ln x Next, take derivative of both sides of the equation with respect to x , d ln

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## This note was uploaded on 09/22/2011 for the course MATH 2144 taught by Professor Pagano during the Fall '08 term at Oklahoma State.

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math9 - Math 2144 Exam II Oct 28 2010 Name Score Please...

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