My Math Forum Directional Derivative and Totally Differentiable

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 March 26th, 2017, 01:44 AM #1 Member   Joined: Nov 2016 From: Kansas Posts: 48 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, 06:32 AM #2 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 1,081 Thanks: 87 del f=f$\displaystyle _{x}$i + f$\displaystyle _{y}$j ck f$\displaystyle _{xy}$ = f$\displaystyle _{yx}$ at (0,0)

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