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March 26th, 2017, 02:44 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 68 Thanks: 0  Directional Derivative and Totally Differentiable
How to show the following: Show that the function: f(x,y) = (x^3 y^3)/(x^2 +y^2) , (x,y) not equal to (0,0) 0, (x,y)=(0,0) has directional vector at (0,0) but not totally differentiable at (0,0) 
March 27th, 2017, 07:32 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,215 Thanks: 91 
del f=f$\displaystyle _{x}$i + f$\displaystyle _{y}$j ck f$\displaystyle _{xy}$ = f$\displaystyle _{yx}$ at (0,0) 

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derivative, differentiable, directional, totally 
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