bruins4777 Posted November 2, 2004 Share Posted November 2, 2004 Anybody know how to figure this out? find the 2nd derivative of this equation: (x^2*y^2)-2X=3 thanks for whoever can help me. I tried it and i get this enourmous equation, but its supposed to cancel really nicely to like 1/something Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 I tried the problem but can't get it to simplify to something nice. I assume you're looking for the second derivative of y with respect to x. First, you solve for y and get y = ((3 + 2x)^1/2)/x. Taking the derivative and applying the chain rule to the expression on the right gives you y' = (1 / ((2x +3)^1/2)(x) ) -( (2x +3)^1/2) /x^2 ) Take the derivative again and you get a horrific expression y'' = [-1/((2x + 3) ^3/2) (x))] - [2 / ((2x + 3)^1/2)(x^2)) ] +[( 2(2x + 3)^1/2)/(x^3)] Couldn't get it more simplified than this. Hope this helps, and sorry! Quote Link to comment Share on other sites More sharing options...
Weekes Head Posted November 2, 2004 Share Posted November 2, 2004 Do your own G*d damned homework! JK (which means I haven't the slightest idea...) Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 2, 2004 Author Share Posted November 2, 2004 I tried the problem but can't get it to simplify to something nice. I assume you're looking for the second derivative of y with respect to x.First, you solve for y and get y = ((3 + 2x)^1/2)/x. Taking the derivative and applying the chain rule to the expression on the right gives you y' = (1 / ((2x +3)^1/2)(x) ) -( (2x +3)^1/2) /x^2 ) Take the derivative again and you get a horrific expression y'' = [-1/((2x + 3) ^3/2) (x))] - [2 / ((2x + 3)^1/2)(x^2)) ] +[( 2(2x + 3)^1/2)/(x^3)] Couldn't get it more simplified than this. Hope this helps, and sorry! <{POST_SNAPBACK}> hmmm u did it different than i did. This is what i did: I found the derivative of the first equation with respect to y and got dy/dx= (1-x*y^2)/(x^2*y) but before that i got (x*y^2)+(y*x^2*dy/dx) =1 Then i found the derivative of that and got 2xy(dy/dx)+(y^2)+second derivative of x^2+2xy(dy/dx) i plugged in the first derivative that i got into this big equation. Then i solved for the 2nd derivative. This got all ugly, but eventually i got. ((3xy^2)-4)/(x^3) soooo yeah. Thats what my final answer was, but i don't think its right. Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 you differentiated implicitly, which should give you the correct result. I overcomplicated the problem. They both should yield the same result, which means my answer when simplified further will reduce, but man, what a mess!! Your first derivative is correct. Taking the second derivative and subtituting the value you got for dy/dx into the y'' equation will give you the correct answer. The answer you've given seems to be very nicely simplified. Are you sure it's not right? Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 2, 2004 Author Share Posted November 2, 2004 you differentiated implicitly, which should give you the correct result. I overcomplicated the problem. They both should yield the same result, which means my answer when simplified further will reduce, but man, what a mess!!Your first derivative is correct. Taking the second derivative and subtituting the value you got for dy/dx into the y'' equation will give you the correct answer. The answer you've given seems to be very nicely simplified. Are you sure it's not right? <{POST_SNAPBACK}> Meh, i guess ur right. It looks right. But the other people i talked to says it wasn't BLAH!!!! SO CONFUSED!! Yeah our quiz was on implicit differiention(sp?). My sister said we'd never see something like this on the AP test, so that takes a load off my shoulders...but i HAVE to do good in this course. I want to take advanced calc(high school version of calc 2) next year. Anyways, i hope this is right. Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 you differentiated implicitly, which should give you the correct result. I overcomplicated the problem. They both should yield the same result, which means my answer when simplified further will reduce, but man, what a mess!!Your first derivative is correct. Taking the second derivative and subtituting the value you got for dy/dx into the y'' equation will give you the correct answer. The answer you've given seems to be very nicely simplified. Are you sure it's not right? <{POST_SNAPBACK}> Meh, i guess ur right. It looks right. But the other people i talked to says it wasn't BLAH!!!! SO CONFUSED!! Yeah our quiz was on implicit differiention(sp?). My sister said we'd never see something like this on the AP test, so that takes a load off my shoulders...but i HAVE to do good in this course. I want to take advanced calc(high school version of calc 2) next year. Anyways, i hope this is right. <{POST_SNAPBACK}> Well, this may not be a great comfort, but seeing this stuff in high school will make any college calc you have to take a lot less intimidating. What you're doing now will take you through Calc I and II in college, meaning you can start taking an applied analysis course (basically a continuation of calc II) right off the bat. Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 2, 2004 Author Share Posted November 2, 2004 you differentiated implicitly, which should give you the correct result. I overcomplicated the problem. They both should yield the same result, which means my answer when simplified further will reduce, but man, what a mess!!Your first derivative is correct. Taking the second derivative and subtituting the value you got for dy/dx into the y'' equation will give you the correct answer. The answer you've given seems to be very nicely simplified. Are you sure it's not right? <{POST_SNAPBACK}> Meh, i guess ur right. It looks right. But the other people i talked to says it wasn't BLAH!!!! SO CONFUSED!! Yeah our quiz was on implicit differiention(sp?). My sister said we'd never see something like this on the AP test, so that takes a load off my shoulders...but i HAVE to do good in this course. I want to take advanced calc(high school version of calc 2) next year. Anyways, i hope this is right. <{POST_SNAPBACK}> Well, this may not be a great comfort, but seeing this stuff in high school will make any college calc you have to take a lot less intimidating. What you're doing now will take you through Calc I and II in college, meaning you can start taking an applied analysis course (basically a continuation of calc II) right off the bat. <{POST_SNAPBACK}> Ya, thats what my sister did. She took the same path i am. Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 (edited) Cool. What are you guys majoring in? Edited November 2, 2004 by Desert Devil Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 2, 2004 Author Share Posted November 2, 2004 Cool. What are you guys majoring in? <{POST_SNAPBACK}> I'm in highschool and i'm a sophmore. My sister majored in double e and just graduated and is working for IBM 7 year difference in age. Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 Wow, a sophomore doing this stuff! You'll be in great shape if you go into physics or ee or me. Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 2, 2004 Author Share Posted November 2, 2004 Wow, a sophomore doing this stuff!You'll be in great shape if you go into physics or ee or me. <{POST_SNAPBACK}> ya i skipped a couple math courses. I know a guy above me who did the same thing above me and he says physics is a breeze with calc. Quote Link to comment Share on other sites More sharing options...
Desert Devil Posted November 2, 2004 Share Posted November 2, 2004 (edited) Wow, a sophomore doing this stuff!You'll be in great shape if you go into physics or ee or me. <{POST_SNAPBACK}> ya i skipped a couple math courses. I know a guy above me who did the same thing above me and he says physics is a breeze with calc. <{POST_SNAPBACK}> Yes, you're supposed to take calculus I concurrently with the first engineering physics, but if you've already been exposed to calc you have a hell of an advantage. Of course, my undergraduate advisor felt that since I'd taken high school calculus I should be in a junior level mechanics course in my first college semester (I'm kinda fuzzy on the details as this was my "vivarin + wild turkey = passing grade" semester). Edited November 2, 2004 by Desert Devil Quote Link to comment Share on other sites More sharing options...
point Posted November 2, 2004 Share Posted November 2, 2004 When you get this down, I need some help with the new tax law. Studying never ends. Quote Link to comment Share on other sites More sharing options...
squishyx Posted November 2, 2004 Share Posted November 2, 2004 i hate derivitives, we learning about implicit differentiation (ahhh the spelling) in my calc class now and im a junior in college! i'd say your in really good shape bruins. i wish i knew how to take derivitives when i was a sophmore in HS. Quote Link to comment Share on other sites More sharing options...
bruins4777 Posted November 3, 2004 Author Share Posted November 3, 2004 i hate derivitives, we learning about implicit differentiation (ahhh the spelling) in my calc class now and im a junior in college! i'd say your in really good shape bruins. i wish i knew how to take derivitives when i was a sophmore in HS. <{POST_SNAPBACK}> i like the basic derivative like x^2 and all those easy ones. But implicit crazy word IS SOOOOO irritating. I always confuse everythign. Its even more annoying when he throws in some of that stupid logarithm stuff and then tangent stuff. My teacher gives the hardest tests. He shows us the tests from last year and they are twice as hard. He's a good teacher, but material is evil!!!! I hope i did good on my test today. Quote Link to comment Share on other sites More sharing options...
MissionHockey Posted November 3, 2004 Share Posted November 3, 2004 Wow, a sophomore doing this stuff!You'll be in great shape if you go into physics or ee or me. <{POST_SNAPBACK}> No kidding, I'm a junior in Algebra 2 (granted, that class is rediculously easy), but most seniors in my school take pre-calc. I'm not even going to be taking a math coarse my senior year so I won't worry about it. Quote Link to comment Share on other sites More sharing options...
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