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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)

June 27th, 2012, 06:02 PM  #2 
Senior Member 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: 
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 
June 28th, 2012, 09:43 PM  #4 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Derivative of x times the absolute value of x
xx behaves exactly like x^2 with the left half reflected about the x axis interestingly, x has no derivative at x=0 but xx has derivative everywhere. http://www.wolframalpha.com/input/?i=pl ... Cx%5E2%29+ 

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