Midterm - Midterm 2 SOLUTIONS MAT 131 Fall 2011 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Midterm 2 SOLUTIONS MAT 131 Fall 2011 1. Calculate the derivatives of the following functions: (a) f ( x ) = 3 x 3 + 4 x 2 + 5 x + 6 x f ( x ) = 3(3 x 2 ) + 4(2 x ) + 5 x + 6(- 1) x- 2 = 9 x 2 + 8 x + 5- 6 x 2 (b) f ( x ) = sin 10 x f ( x ) = 10(sin x ) 9 d dx sin x = 10sin 9 x cos x (c) f ( x ) = x 2 + 1 x + 5 f ( x ) = ( x + 5)(2 x )- ( x 2 + 1)(1) ( x + 5) 2 = 2 x 2 + 10 x- x 2- 1 ( x + 5) 2 = x 2 + 10 x- 1 ( x + 5) 2 (d) f ( x ) = 3 x log 3 ( x + 3) f ( x ) = 3 x d dx ln( x + 3) ln3 + log 3 ( x + 3) d dx 3 x = 3 x 1 (ln3)( x + 3) + 3 x (ln3)log 3 ( x + 3) = 3 x (ln3)( x + 3) + 3 x ln( x + 3) (e) f ( x ) = arctan( x 2 + 1) f ( x ) = 1 1 + ( x 2 + 1) 2 2 x = 2 x x 4 + 2 x 2 + 2 (f) f ( x ) = x sin x First we set y = f ( x ) and take a logarithm: ln y = ln( x sin x ) = sin x ln x . Next we differentiate both sides implicitly with respect to x : y y = sin x x + cos x ln x. Then we multiply both sides by y and replace y with f ( x ): f ( x ) = x sin x sin x x + cos x ln x MAT 131 Fall 2011...
View Full Document

This note was uploaded on 01/13/2012 for the course MAT 131 taught by Professor Christopherbay during the Fall '08 term at SUNY Stony Brook.

Page1 / 5

Midterm - Midterm 2 SOLUTIONS MAT 131 Fall 2011 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

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