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: 20,370 Thanks: 2007 
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: 2,073 Thanks: 843 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  

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differential, partial 
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