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October 25th, 2014, 09:04 PM  #1 
Newbie Joined: Jul 2014 From: Brazil Posts: 8 Thanks: 0  How to find f(x)=1/x using the fundamental theorem of calculus?
I know how to find it using the shortcut rule, which is basically $\displaystyle f(x)=1/x$ =$\displaystyle x^1$ =$\displaystyle x^2$ But the question is asking me to find the derivative using the fundamental theorem of calculus and I seriously have no idea how and I'm honestly really frustrated because I've been stuck on this for two days now. If you have any idea on how to solve it using the theorem, then I'd really appreciate the help ;; The formula is supposed to be f(x) = lim h approaches 0 $\displaystyle f(x+h)  f(x)/h$ Last edited by Anon321; October 25th, 2014 at 09:13 PM. 
October 25th, 2014, 09:31 PM  #2 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry 
$\displaystyle f(x)=\frac{1}{x}$ $\displaystyle \lim_{h\to0}\frac{f(x+h)f(x)}{h}$ $\displaystyle =\lim_{h\to0}\frac{\frac{1}{x+h}\frac{1}{x}}{h}$ $\displaystyle =\lim_{h\to0}\frac{\frac{x}{x(x+h)}\frac{x+h}{x(x+h)}}{h}$ $\displaystyle =\lim_{h\to0}\frac{x(x+h)}{xh(x+h)}$ $\displaystyle =\lim_{h\to0}\frac{\cancel{h}}{x\cancel{h}(x+h)}$ $\displaystyle =\lim_{h\to0}\frac{1}{x(x+h)}$ Substitute h = 0, and you will get $\displaystyle \frac{1}{x^2}$ Last edited by Monox D. IFly; October 25th, 2014 at 09:48 PM. 
October 25th, 2014, 09:48 PM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff.  
October 30th, 2014, 08:32 AM  #4 
Newbie Joined: Oct 2014 From: earth Posts: 3 Thanks: 0  Last edited by skipjack; November 1st, 2014 at 09:40 AM. 
October 30th, 2014, 01:12 PM  #5  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
 
October 30th, 2014, 06:09 PM  #6  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra  Quote:
Last edited by skipjack; November 1st, 2014 at 09:42 AM.  
October 30th, 2014, 11:12 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
Once again, please remain on topic.

October 30th, 2014, 11:14 PM  #8 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  I just reported his post for being combative and argumentative.
Last edited by skipjack; November 1st, 2014 at 09:45 AM. 
October 31st, 2014, 06:12 AM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
At the risk of straying further off topic, I would reply to your combative and argumentative private message, but you don't see fit to allow people to send you any private messages so I'll just have to ignore it. [Note by moderator: I've removed the offtopic content with v8archie's consent.] Last edited by skipjack; November 1st, 2014 at 09:51 AM. 

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calculus, find, fundamental, fx1 or x, theorem 
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