Question

Implicit differentiation, just some general big idea questions

Answer 1

so we are looking for the derivative at a point on a curve, that is the big picture idea for implicit, correct?
why does dx/dx equal the value of 1?

Answer 2

first Q: I would not agree that that is the concept of implicit differentiation
second Q: dx/dx relates the rate change of x with respect to x
logically this is always one
it's like asking, "for every x I move, how many x's do I move"
the answer is always one

Answer 3

the point of finding a rate change through implicit differentiation here is one of pure practicality

Answer 4

we could solve this sucker for y, then take the derivative, but we would have to apply more mores than if we do this implicitly

Answer 5

I know that you can take the derivative of this function both explicitly and implicity.

Answer 6

either way we would get the same result
with cases like y=x^4+x^2+1 though if we tried to solve this for x we would wind up with 2 \(\pm\) signs, which is confusing

Answer 7

I also, know that there are many equations that are either difficult or impossible to solve for y explicitly in terms of x (so this method is more for your convenience)

Answer 8

let me get you a good link from MIT on this.... one sec

Answer 9

I know that in a calculus course, implicit is probably an intro to a diff eqs course. Am I wrong to think that?

Answer 10

er... sort of...
all calc is an intro do DE's, so yeah, implicity differentiation is a part of it, but when you learn seperation of variables, or the constant of indefinite integration, that is closer to an intro to DE's in my opinoin

anyway, here is a great class on implicit differentiation

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-b-implicit-differentiation-and-inverse-functions/session-14-examples-of-implicit-differentiation/

Answer 11

implicit*

Answer 12

Thanks, I will check it out.

Answer 13

please do, and not the second section is exactly about the equation of a circle

Answer 14

and note...*

Answer 15

Thanks, I just finished watching it. Does the study group selection, put them in an openstudy study group?

Answer 16

Do you know if there are any physics lectures? I will be taking Physics Honors for the next two semesters and am looking for a good resource other than khanacademy