Problem Set 08s

# F x log 5 xe x solution b 1 d 1 f x

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ྎ − sin x ln x ⎥ྏ y ⎣ྏ x ⎦ྏ cos x − x sin x ln x ⎤ྏ ⎡ྎ y ' = x cos x ⎢ྎ ⎥ྏ x ⎣ྏ ⎦ྏ d. f ( x ) = log 5 ( xe x ) Solution: b. 1 d 1 f (' x ) = x ( xe x ) = xe x ln 5 (e x + xe x ) xe ln 5 dx e x + xe x =x xe ln 5 1+ x f ' ( x) = x ln 5 ln x y = (sin x ) Solution: 1 ) Hung Nguyen c. Problem Set 08 Solution GE 207C 3.6 Derivatives of Logarithmic Functions ln x a. f ( x ) = 2 + ln x y = (sin x ) Solution: ln y = ln (sin x ln x ) = ( ln x ) ln (sin x ) f ( x) = 2 + ln x !1\$ 1 1 y ' = ln (sin x ) + ln x # & cos x 1 1 ⎞ྏ 1 −1 / 2 ⎛ྎ " sin x % y x f ' ( x) = (2 + ln x ) ⎜ྎ 0 + ⎟ྏ = 2 x ⎠ྏ 2 x 2 + ln x ⎝ྎ ! cos x \$ ln(sin x ) = + ( ln x ) # & 1 " sin x % x f ' ( x) = 2 x 2 + ln x 1 ln(sin x ) y' = + ( ln x ) c...
View Full Document

## This document was uploaded on 02/27/2014 for the course M 408c at University of Texas.

Ask a homework question - tutors are online