# Fun with Integral Calculus, or I'm totally not getting laid. **URL:** \ **Category:** Shift518 Automotive\ **Created:** [January 28, 2009, 5:22pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653 "2009-01-28T17:22:31Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![1320-20V](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/1320-20v/32/6474_2.png) [@1320-20V](https://forums.speedlife.net/u/1320-20V)\ **Post date:** [January 28, 2009, 5:22pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/1 "2009-01-28T17:22:31Z")
I think I fully understand this problem. y=2x(x^2+1)^1/2 Find y’ It is a combination of the product rule, the chain rule and U-substitution as I see it. First the product rule. Two terms F,G. F=2x G=(x^2+1)^1/2 Therefore f(g)’ = f’g+g’f (the product rule) But what is g **’**? g’ seems to be a combination of the chain rule and u-substitution. u = x^2+1 is a function all of its own, something is squared and then one is added. Then the product of u is operated on by another separate function that takes the square root of the output of the u function. **The U substitution rule, as I see it is almost another way of looking at the chain rule???** I think a few moments ago I fully understood the meaning of the chain rule. I will try to sum it up in this analogy: The chain rule differentiates multiple related functions. For example: **Y** olonda buys 3 times as many potatoes as **X** ander. And **X** ander buys 2 times as many potatoes as **U** lysses. How many more potatoes does **Y** olonda have than **U** lysses? d **Y** /d **X** = (d **Y** /d **U** ) (d **U** /d **X** ) **This seems to be explaining the commutative property of multiplication**? ( when all of the terms are functions instead of numbers ) But you can’t seem to use the chain rule without a new variable “u” So we replace the one function “G” with two functions, “U” and (u)^1/2 Both are easy to differentiate. The “u substitution rule” is d/dx [u^n] = n(u)^n-1 (du) **This to me seems to be directly relating The chain rule, the product rule, u-substitution, and the power rule inside the u substitution rule itself.** This implies to me that any complex function can be factored down into smaller composite functions, and then handled as multiple smaller units. Although it seems as if in doing that the order of operations of the original function seems to be lost, but perhaps I have just not fully understood that part of the rules of differentiation. ---
**Author:** ![SXY\_TIME](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/sxy_time/32/6293_2.png) [@SXY\_TIME](https://forums.speedlife.net/u/SXY_TIME)\ **Post date:** [January 28, 2009, 5:24pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/2 "2009-01-28T17:24:04Z")
yea having to take this shit as a night class is awful… ---
**Author:** ![Shady](https://avatars.discourse-cdn.com/v4/letter/s/6de8d8/32.png) [@Shady](https://forums.speedlife.net/u/Shady)\ **Post date:** [January 28, 2009, 5:25pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/3 "2009-01-28T17:25:07Z")
i dident read any of that I saw a formula and immediately thought of keanu reaves in the day the earth stood still fixing the old dudes equation on the chalk board and my head immediatly hurting ---
**Author:** ![LKSi](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/lksi/32/6316_2.png) [@LKSi](https://forums.speedlife.net/u/LKSi)\ **Post date:** [January 28, 2009, 5:25pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/4 "2009-01-28T17:25:48Z")
I wish I remembered ANYTHING from the 4 calc courses I’ve taken… but I am no help. good luck. ---
**Author:** ![Sully93vr4](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/sully93vr4/32/6278_2.png) [@Sully93vr4](https://forums.speedlife.net/u/Sully93vr4)\ **Post date:** [January 28, 2009, 5:25pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/5 "2009-01-28T17:25:53Z")
chain rule integrals, lol. I wish I was only doing that shit. ---
**Author:** ![SXY\_TIME](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/sxy_time/32/6293_2.png) [@SXY\_TIME](https://forums.speedlife.net/u/SXY_TIME)\ **Post date:** [January 28, 2009, 5:26pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/6 "2009-01-28T17:26:35Z")
oh god keanu is such a horrible actor lol “whooaaaaaaaaaaa maaaaaaaaannn” he talks like a fuckin stoner ---
**Author:** ![1320-20V](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/1320-20v/32/6474_2.png) [@1320-20V](https://forums.speedlife.net/u/1320-20V)\ **Post date:** [January 28, 2009, 5:27pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/7 "2009-01-28T17:27:57Z")
> [@Patriotic Hummer H3](https://forums.speedlife.net/t/patriotic-hummer-h3/13163/78): > > yea having to take this shit as a night class is awful… Do you get anything for the exams at SCCC? I got nothing but a pencil, no rules, no calculators, no formula sheets, nada. ---
**Author:** ![SXY\_TIME](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/sxy_time/32/6293_2.png) [@SXY\_TIME](https://forums.speedlife.net/u/SXY_TIME)\ **Post date:** [January 28, 2009, 5:34pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/8 "2009-01-28T17:34:58Z")
> [@Big Ben crashes motorcycle](https://forums.speedlife.net/t/big-ben-crashes-motorcycle/13213/10): > > Do you get anything for the exams at SCCC? > > I got nothing but a pencil, no rules, no calculators, no formula sheets, nada. havent had an exam in it yet…just started the semester but the professor said she might provide a formula sheet and we can still use our calcs ---
**Author:** ![GermanPSI](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/germanpsi/32/6353_2.png) [@GermanPSI](https://forums.speedlife.net/u/GermanPSI)\ **Post date:** [January 28, 2009, 5:41pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/9 "2009-01-28T17:41:12Z")
> [@SXY TIME"](#): > > havent had an exam in it yet…just started the semester but the professor said she might provide a formula sheet and we can still use our calcs whats your major guys major ---
**Author:** ![SXY\_TIME](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/sxy_time/32/6293_2.png) [@SXY\_TIME](https://forums.speedlife.net/u/SXY_TIME)\ **Post date:** [January 28, 2009, 5:46pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/10 "2009-01-28T17:46:23Z")
currently im getting my associates in science then eventually i’ll be going to med school…fun shit ( i dont even need calc for alb med college but i just found that out lol ---
**Author:** ![1320-20V](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/1320-20v/32/6474_2.png) [@1320-20V](https://forums.speedlife.net/u/1320-20V)\ **Post date:** [January 28, 2009, 6:01pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/11 "2009-01-28T18:01:03Z")
BS Mechanical Engineering Technology. Second semester of my Jr. year. ---
**Author:** ![w.tungsten](https://avatars.discourse-cdn.com/v4/letter/w/7bcc69/32.png) [@w.tungsten](https://forums.speedlife.net/u/w.tungsten)\ **Post date:** [January 28, 2009, 6:38pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/12 "2009-01-28T18:38:23Z")
I’ll join in on this shit. pretty sure u-substitution is used for integrals not derivatives. At least I think so. Well your y’ should be: y’ = 2(X^2 +1)^(1/2) + (2X^2)(X^2 +1)^(-1/2) ---
**Author:** ![1320-20V](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/1320-20v/32/6474_2.png) [@1320-20V](https://forums.speedlife.net/u/1320-20V)\ **Post date:** [January 28, 2009, 6:45pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/13 "2009-01-28T18:45:52Z")
> [@TW or WTT: 2000 LS Integra](https://forums.speedlife.net/t/tw-or-wtt-2000-ls-integra/13233/3): > > I’ll join in on this shit. > > pretty sure u-substitution is used for integrals not derivatives. At least I think so. > > Well your y’ should be: > y’ = 2(X^2 +1)^(1/2) + (2X^2)(X^2 +1)^(-1/2) Almost! y’= 2[(x^2+1)^1/2]+[(2x^2)/(x^2+1)^ **1/2**] Your second “radical” should not be negative. Did you just do that out on paper? Did you use the chain rule alone with no U-sub? Feel free to move out here and be my full time Calc tutor! I have an extra room! LOL ---
**Author:** ![psi2high](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/psi2high/32/6320_2.png) [@psi2high](https://forums.speedlife.net/u/psi2high)\ **Post date:** [January 28, 2009, 6:46pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/14 "2009-01-28T18:46:32Z")
Ha ha math will not help you in med school ---
**Author:** ![JClark](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/jclark/32/6309_2.png) [@JClark](https://forums.speedlife.net/u/JClark)\ **Post date:** [January 28, 2009, 6:49pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/15 "2009-01-28T18:49:03Z")
Oh noooww I remember why I changed majors… ---
**Author:** ![mcflurry](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/mcflurry/32/6468_2.png) [@mcflurry](https://forums.speedlife.net/u/mcflurry)\ **Post date:** [January 28, 2009, 6:52pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/16 "2009-01-28T18:52:57Z")
yea glad i aint gotta take shit ---
**Author:** ![psi2high](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/psi2high/32/6320_2.png) [@psi2high](https://forums.speedlife.net/u/psi2high)\ **Post date:** [January 28, 2009, 6:55pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/17 "2009-01-28T18:55:32Z")
Indeed ---
**Author:** ![Mike3](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/mike3/32/6350_2.png) [@Mike3](https://forums.speedlife.net/u/Mike3)\ **Post date:** [January 28, 2009, 7:05pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/18 "2009-01-28T19:05:12Z")
> [@Suggestions on new case?](https://forums.speedlife.net/t/suggestions-on-new-case/13217/7): > > chain rule integrals, lol. I wish I was only doing that shit. Haha +1 ---
**Author:** ![w.tungsten](https://avatars.discourse-cdn.com/v4/letter/w/7bcc69/32.png) [@w.tungsten](https://forums.speedlife.net/u/w.tungsten)\ **Post date:** [January 28, 2009, 7:07pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/19 "2009-01-28T19:07:22Z")
Yeah, just chain rule no u-sub. I don’t think you can do u-sub with derivatives, I may be wrong. Paper is the ONLY way to go. haha I’m pretty sure it’s negative since you bring it down as a coefficient then minus one from the exponent. like y = X^2 y’ = 2X^(2-1) = 2x^1 = 2X Dude, I’m terrible at teaching, just doing. \*oh lolololol we have the same answer. You have (X^2+1)^(1/2) as a denominator. It’s the same as a negative exponent. \*\*side note, do you drive a ae86 by any chance. I saw the 20v so I jumped into the thread… ---
**Author:** ![dkid15](https://yyz2.discourse-cdn.com/flex034/user_avatar/forums.speedlife.net/dkid15/32/6398_2.png) [@dkid15](https://forums.speedlife.net/u/dkid15)\ **Post date:** [January 28, 2009, 7:43pm UTC](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653/20 "2009-01-28T19:43:20Z")
Tungsten is right it is a negative. However your version of chain rule is similar to something called quotient rule. You have one large chain rule problem and you do not neccesarily have to substitute because its not that complex of a problem. 1. 2x(x^2 +1)^1/2 is you equation next what you need to do is label all terms. 2. so you have 2x (1), x^2 +1 (2) going to have to take the derivative inside seperately. and you have the (1/2) 3. There are now 3 total parts 4. I would go through it but i just found out your answer is correct. Damn. 5. For future reference you could have substituted by make u = x^2+1 and du = 2xdx but i would only do that to get the anti derivative. [Next page](https://forums.speedlife.net/t/fun-with-integral-calculus-or-im-totally-not-getting-laid/241653.md?page=2)