## 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)

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)

# See Also:

Download article: lec1.pdf (1.0 MB)

Download mit1801f06_jerison_lec01_01.m4v (Video - generic video source 113.9 MB)

Download mit1801f06_jerison_lec01_01.rm (Video - generic video source 82.4 MB)

Download mit1801f06_jerison_lec01_01.flv (Video 150.1 MB)

Download mit1801f06_jerison_lec01_01.wmv (Video 439.9 MB)

# Related content

# 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**to describe your request and upload the data.**

__ticket system__*Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.*

# Link this page

Would you like to put a link to this lecture on your homepage?

Go ahead! Copy the HTML snippet !

## Reviews and comments:

s0uvik das, October 20, 2011 at 9:17 a.m.:sir u r g0d t0 me

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.

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

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

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

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

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

## Write your own review or comment: