Lecture 1: Derivatives, slope, velocity, rate of change
author: David Jerison,
Center for Future Civic Media, Massachusetts Institute of Technology, MIT
recorded by: Massachusetts Institute of Technology, MIT
published: June 28, 2010, recorded: September 2006, views: 40817
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)
recorded by: Massachusetts Institute of Technology, MIT
published: June 28, 2010, recorded: September 2006, views: 40817
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)
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Reviews and comments:
sir u r g0d t0 me
I am a bit curious about the calculation of the change in f (delta f), and the y coordinates of Q. Since Y= f(x), I suppose the vertical change in y (delta y), should also be change in f(x) or delta f(x) and not just change in f (delta f).
I will be grateful if someone can elaborate on this a little bit.
becaus f is a fung. this is changing y respect to x so this fuun.cant change
Argh! I was able to use the download links the first time I loaded this page, but now the video player is the full width of the page and is covering up all those links!
(Y + delta Y)/x+dx is also right,
However f(x) + delta f(x) says nothing to solve the problem for delta f(x) not is easy to be found,
but we can calculate directly the value of Y thought {f(x)+delta f(x)}=f(x+dx),
The reason is because we change all values in x variables to simplify formula and calculate y in terms of x.
then
dy . (y+dy)-y . [f(x)+df(x)]-f(x)
-- = ---------- = -----------------
dx . (x+dx)-x . . (x + dx) - x
but if [f(x)+df(x)] = f(x+dx)
then:
dy . [f(x+dx)-f(x)]
-- = --------------
dx . [(x+dx)-x]
is a step to solve the problem,
and limit when dx tends to 0:
. . . . . . f(x+dx)-f(x)
y' = Lim --------------
. . . dx->0 . . . dx
because it solve the problem
ordering y in terms of x
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