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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online