Okay, I know there are a lot of people on this forum who are really really good at math. I'm decent- I got a 108% in precal last year. That's incredible for me. But I say I'm decent because there's one thing I don't understand.
Implicit differentiation.
I'm completely, hopelessly, helplessly lost. Does anyone out there know of a way to get me to understand this quicker?
Posted by xtownaga (Member # 7187) on :
Not sure if you've seen it, but Wikipedia has an article that deals with it a bit.
I can't think of a good way to explain it online though, but if I have time later and someone hasn't beaten me to it I can try.
Posted by KPhysicsGeek (Member # 8655) on :
You are probably making it more difficult than it is. The basic premise is that we can find derivatives of functions even why y isn't completely seperated out. The key is remembering how to treat a function with y; basically you treat y like any function of x using the chain rule. Depending on the question you may want to solve for dy/dx or find the derivative for a spefic value.
Here is a quick example:
sin(2x-y2) = 17y d/dx(sin(2x-2y)) = d/dx(17y) cos(x-y)d/dx(2x-2y) (chain rule) = 17(dy/dx) cos(x-y)(2-2dy/dx) = 17(dy/dx) multiply through 2cos(x-y)-2dy/dx(cos(x-y)) = 17(dy/dx) move dy/dx's to one side -2dy/dx(cos(x-y)) - 17(dy/dx) = -2 cos(x-y) divide out leaving dy/dx dy/dx = -2cos(x-y)/(-2cos(x-y)-17)
The whole key is remembering the chain rule and getting dy/dx's on one side.
Ah, 2gether, what an awesome parody band
Posted by pfresh85 (Member # 8085) on :
Yeah. It's like KPhysicsGeek said. You just differentiate each side with resepect to the variables. Then you try and get all the dy/dx's to one side. It's not too bad.
Posted by The Rabbit (Member # 671) on :
quote:I know there are a lot of people on this forum who are really really good at math. I'm decent- I got a 108% in precal last year.
You may be decent at math but your statement suggest that you precal instructor was not.
Posted by genius00345 (Member # 8206) on :
It's probably a little thing I like to call 'extra credit'.
Posted by Shigosei (Member # 3831) on :
If it helps, remember that y is actually y(x). So when you differentiate a function with y in it, you're actually differentiating a function within a function. So the derivative of [y(x)]^2 is 2y(x)*y'(x), or 2y(x)*dy/dx depending on whether you're using Liebnitz or Newton notation. You're using the chain rule here, as others have mentioned.
Once you've done the differentiation, you can solve the resulting equation for dy/dx to find the derivative of y.
Posted by The Rabbit (Member # 671) on :
quote:Originally posted by genius00345: It's probably a little thing I like to call 'extra credit'.
Yes but then that begs the question, 108% of what? Certainly not possible points or maximum points. 108% of what?
Posted by HollowEarth (Member # 2586) on :
It should be pointed out that you can't always get an explict expression for dy/dx even doing implicit differentiation. (ie you can't always solve for dy/dx)
Posted by fugu13 (Member # 2859) on :
108% of maximal points on required work.
Posted by Icarus (Member # 3162) on :
quote:It's probably a little thing I like to call 'extra credit'.
If enough extra credit is being given to average 108%, then a sickening amount of grade-inflation is going on.
Unlike a lot of teachers, I am not totally opposed to extra credit. But extra credit should not be capable of raising your average by as many as eight points.
I agree with Rabbit.
Posted by Tinros (Member # 8328) on :
The class was weighted- as is Calculus, Physics, all AP classes, Honors English 3... you get the drift. My actual "grade" was a 98% of the maximum points, WITHOUT the 10% weight that they add to the report card. My precal teacher was the best teacher I've ever had- she's one of the NHS advisers, and has been teacher of the year quite a few times. She's incredible at what she does- where other teachers have a hard time getting students to understand things, she just got them to click with me. Keep in mind, most of my grades cluster around 97%-99%, without weights, and I always have a 100% in band, because it's a participation grade. But my teachers don't offer extra credit... I just did really well in precal.
Posted by Tinros (Member # 8328) on :
Actually, that website really helped. Our teacher explained it in about 5 minutes, but never really told us when to use the d/dx, when to find a regular derivative, and nothing made sense. I think I get it now. Thanks.
Posted by Eldrad (Member # 8578) on :
quote:Originally posted by KPhysicsGeek: You are probably making it more difficult than it is. The basic premise is that we can find derivatives of functions even why y isn't completely seperated out. The key is remembering how to treat a function with y; basically you treat y like any function of x using the chain rule. Depending on the question you may want to solve for dy/dx or find the derivative for a spefic value.
Here is a quick example:
sin(2x-y2) = 17y d/dx(sin(2x-2y)) = d/dx(17y) cos(x-y)d/dx(2x-2y) (chain rule) = 17(dy/dx) cos(x-y)(2-2dy/dx) = 17(dy/dx) multiply through 2cos(x-y)-2dy/dx(cos(x-y)) = 17(dy/dx) move dy/dx's to one side -2dy/dx(cos(x-y)) - 17(dy/dx) = -2 cos(x-y) divide out leaving dy/dx dy/dx = -2cos(x-y)/(-2cos(x-y)-17)
The whole key is remembering the chain rule and getting dy/dx's on one side.
When you took the derivative of sin(2x-2y), you forgot to make it cos(2x-2y) instead of cos(x-y) multiplied by everything else with the chain rule.
[ October 18, 2005, 10:30 PM: Message edited by: Eldrad ]
Posted by Art Vandelay (Member # 8690) on :
2gether reference. Awesome.
"Yo, robin's egg blue is my color b@*&h!"
Posted by pfresh85 (Member # 8085) on :
A Calculus-based anecdote of sorts: Three friends from my Calculus BC AP class (as well as the Physics C AP class) and I started a boy band known as the Gr4duates (the 4 was because we graduated in 2004). Our hit song was "Integrate My Heart," although the lyrics have long escaped me now. The Gr4duates really didn't go very far though, aside from doing group karaoke (singing Backstreet Boys and N'Sync songs) at our Project Graduation.
Posted by Eruve Nandiriel (Member # 5677) on :
OH GOD!!! NOT THE "C-WORD"!!!
*runs from thread screaming*
Posted by Shigosei (Member # 3831) on :
+C
Posted by HollowEarth (Member # 2586) on :
At functions' party, everybody is having fun. You can see Square Root and Addition grooving all around, Logarithm is boozing with some friends, Cosine is chatting some girls up. But there, in a dark corner, Exponential is sitting all by himself, sad and blue, his eyes fixed on the ground. Tangent and Arc Tangent approacch him and say: "Come on, what you're doing there! It's a party, you gotta have fun! Just integrate with the others!". Exponential glances them even more depressed and replies: "and how exactly would that change things?"
Posted by FrogGirl (Member # 8747) on :
Random question: you don't live in MD do you Tinros?
Posted by Tinros (Member # 8328) on :
No, I'm in Ohio. Why?
Posted by Mike (Member # 55) on :
HollowEarth: Posted by rivka (Member # 4859) on :
quote:Originally posted by Icarus: Unlike a lot of teachers, I am not totally opposed to extra credit. But extra credit should not be capable of raising your average by as many as eight points.
![[ROFL]](graemlins/rofl.gif)
![[Wink]](wink.gif)