
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 25th, 2014, 10:04 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 10:13 PM. 
October 25th, 2014, 10:31 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 10:48 PM. 
October 25th, 2014, 10:48 PM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,345 Thanks: 986 Math Focus: Wibbly wobbly timeywimey stuff.  
October 30th, 2014, 09:32 AM  #4 
Newbie Joined: Oct 2014 From: earth Posts: 3 Thanks: 0  Last edited by skipjack; November 1st, 2014 at 10:40 AM. 
October 30th, 2014, 02:12 PM  #5  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
 
October 30th, 2014, 07:09 PM  #6  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra  Quote:
Last edited by skipjack; November 1st, 2014 at 10:42 AM.  
October 31st, 2014, 12:12 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond 
Once again, please remain on topic.

October 31st, 2014, 12:14 AM  #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 10:45 AM. 
October 31st, 2014, 07:12 AM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 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 10:51 AM. 

Tags 
calculus, find, fundamental, fx1 or x, theorem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fundamental Theorem of Calculus  bonildo  Calculus  2  September 11th, 2014 11:00 AM 
Fundamental theorem of calculus  Mr Davis 97  Calculus  6  June 5th, 2014 03:29 PM 
Fundamental theorem of calculus  layd33foxx  Calculus  3  December 12th, 2011 08:32 PM 
fundamental theorem of calculus  riotsandravess  Calculus  3  November 25th, 2010 01:44 PM 
Fundamental Theorem of Calculus  Aurica  Calculus  1  June 14th, 2009 09:04 AM 