## 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: 40557
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)
Categories

# Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

1 s0uvik das , October 20, 2011 at 9:17 a.m.:

sir u r g0d t0 me

2 Nicholas Adu-Gyamfi, November 3, 2011 at 5:45 p.m.:

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.

3 sb.bartwal, September 17, 2013 at 9:52 a.m.:

becaus f is a fung. this is changing y respect to x so this fuun.cant change

4 Alan, November 26, 2013 at 5:59 a.m.:

5 Jorge, January 13, 2016 at 4:55 p.m.:

(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

6 عراقي, December 31, 2016 at 4:13 a.m.:

طكينه

7 Muhammad Hamza Awan , December 10, 2017 at 10:32 p.m.:

Hello sir, I'm a student from LUMS currently pursuing a career in ACF. I have watched your lecture video on derivatives but it stopped after 13 minutes.
I want to watch your lectures as I want to have a better understanding with my course.Do I have to pay for thes3 lectures?
Actually I don't know the exact procedure so kindly guide me