My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum

LinkBack Thread Tools Display Modes
March 26th, 2017, 02:44 AM   #1
Joined: Nov 2016
From: Kansas

Posts: 73
Thanks: 1

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)
ZMD is offline  
March 27th, 2017, 07:32 AM   #2
Senior Member
Joined: Mar 2015
From: New Jersey

Posts: 1,648
Thanks: 119

del f=f$\displaystyle _{x}$i + f$\displaystyle _{y}$j

ck f$\displaystyle _{xy}$ = f$\displaystyle _{yx}$

at (0,0)
zylo is online now  

  My Math Forum > College Math Forum > Real Analysis

derivative, differentiable, directional, totally

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Directional derivative problem motant Calculus 5 June 16th, 2015 03:15 AM
Lie Derivative (directional derivative proof) supaman5 Linear Algebra 0 November 26th, 2012 11:14 AM
Directional derivative chrill3123 Calculus 5 April 21st, 2012 07:51 PM
Directional derivative (gradient given) dk1702 Abstract Algebra 0 July 20th, 2010 10:58 PM
Directional Derivative Problem howcome123 Calculus 1 June 3rd, 2010 09:57 AM

Copyright © 2019 My Math Forum. All rights reserved.