My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 27th, 2012, 04:39 PM   #1
Newbie
 
Joined: Jun 2012

Posts: 1
Thanks: 0

Derivative of x times the absolute value of x

Ok...so what is the derivative of: h(x) = x*|x| at (0,0)
telmotelmo is offline  
 
June 27th, 2012, 06:02 PM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Derivative of x times the absolute value of x

We are given:



Using the product, power and chain rules, we find:



Hence:

MarkFL is offline  
June 27th, 2012, 09:51 PM   #3
Newbie
 
Joined: May 2012

Posts: 3
Thanks: 0

Re: Derivative of x times the absolute value of x

y=xmodx If x is positive modx=x so y=x^2 and derivative=2x
If x is negative modx=-x so y= -x^2 and derivative= -2x
biffboy is offline  
June 28th, 2012, 09:43 PM   #4
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: Derivative of x times the absolute value of x

x|x| behaves exactly like x^2 with the left half reflected about the -x axis

interestingly, |x| has no derivative at x=0 but x|x| has derivative everywhere.

http://www.wolframalpha.com/input/?i=pl ... Cx%5E2%29+
agentredlum is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
absolute, derivative, times



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find the absolute minimum and absolute maximum. corleoneee Calculus 5 October 22nd, 2013 12:31 AM
Absolute Value Inequality with Absolute Values on Both Sides shiseonji Algebra 2 September 24th, 2013 08:36 AM
how many times is a bigger then d gelatine1 Algebra 2 December 29th, 2012 12:09 AM
Critical Numbers / Absolute Extremas / First Derivative Test RMG46 Calculus 1 October 24th, 2011 10:00 AM
0 six times + 1 five times Sara so Algebra 3 January 4th, 2011 11:27 AM





Copyright © 2019 My Math Forum. All rights reserved.