December 13th, 2018, 12:40 AM  #1 
Newbie Joined: Dec 2018 From: Sudan Posts: 1 Thanks: 0  Partial Differential
Hello, if f is a function of x, how come this is true: I could not remember this rule of partial differentiation. Any help? Thanks 
December 13th, 2018, 03:27 AM  #2 
Newbie Joined: Dec 2018 From: San Deigo Posts: 1 Thanks: 0 Math Focus: Algebra 
Notice that f(0+0)=f(0)+f(0) which implies that f(0)=0. Then, f′(0)=limh→0f(h)−f(0)h=limh→0f(h)h. Using f′(x)=limh→0f(x+h)−f(x)h=limh→0f(x)+f(h)+x h(x+h)−f(x)h So f′(x)=limh→0f(h)h+limh→0xh(x+h)h=f′(0)+x2 So f′(x)=−1+x2 Finally, f′′(x)=2x. 
December 13th, 2018, 06:30 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,751 Thanks: 2135 
The image should be uploaded instead of linked to.

December 13th, 2018, 02:12 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,203 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  

Tags 
differential, partial 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Partial Differential Differential Equations  rishav.roy10  Differential Equations  0  August 21st, 2013 05:59 AM 
Partial Differential..!  ivector  Differential Equations  4  July 24th, 2013 09:51 PM 
partial differential equations help  roshe  Differential Equations  0  April 21st, 2013 10:26 PM 
partial differential  luketapis  Differential Equations  2  March 27th, 2012 07:45 AM 
partial differential equation  sixflags11804  Differential Equations  1  September 29th, 2008 01:26 PM 