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 March 2nd, 2016, 06:18 PM #1 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 Confusion over the Fundamental Theorem So I've been looking at ways to rewrite arcsin, and I found this: arcsin (x/a) + C = the integral of 1 over the square root of a^2 minus x^2 dx This is correct But when I try to graph the DERIVATIVE of arcsin (x/a), I expected it to be the same graph as 1 over the square root of a^2 minus x^2 dx, which is the same thing as above but without the integral. However, this does not work, instead the a^2 must be a 1 for them to be the same. Why is this? March 2nd, 2016, 06:39 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra Are you graphing it correctly, or is your derivative incorrect? ${\mathrm d \over \mathrm d x}\arcsin {x \over a} = \frac1a {1 \over \sqrt{1- \left({x \over a}\right)^2}}$ March 2nd, 2016, 06:45 PM   #3
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What value did you use for the constant, $a$? I used $a=3$, and graphed both the derivative of $\arcsin(x/3)$ and $\dfrac{1}{\sqrt{9-x^2}}$.

Note that I added 1 to the square root function, effectively shifting it up one unit so it could be seen ... without doing so, the two graphs were superimposed.
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Last edited by skipjack; March 3rd, 2016 at 01:01 AM. March 2nd, 2016, 08:48 PM #4 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 I see what I've done wrong, sorry guys, thanks for always offering help though!! Tags confusion, fundamental, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Omnipotent Calculus 6 November 30th, 2014 06:16 AM Omnipotent Calculus 1 November 27th, 2014 01:11 PM Mr Davis 97 Calculus 6 June 5th, 2014 02:29 PM ray Algebra 6 April 22nd, 2012 03:50 AM E.L.Kim Calculus 1 July 26th, 2009 01:42 PM

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