- #1

Jhenrique

- 685

- 4

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Jhenrique
- Start date

- #1

Jhenrique

- 685

- 4

- #2

lurflurf

Homework Helper

- 2,452

- 148

A common situation would be if the movement is constrained so that

f(x,y,t)=0

by the Implicit function theorem we can think of x and y as each being functions of time, or as being functions of each other.

- #3

chogg

- 129

- 10

I would add the following link, which is the most beautiful explanation of partial derivatives which I've encountered.

http://www.av8n.com/physics/partial-derivative.htm

- #4

Jhenrique

- 685

- 4

Do you mean the derivative or the differential?

differential in the inverse sense of integral, ie, "the differential of f wrt to x results the derivative of f"...

I would add the following link, which is the most beautiful explanation of partial derivatives which I've encountered.

http://www.av8n.com/physics/partial-derivative.htm

His answer did not clear anything to me. You text-link is very big, gives to summarize?

- #5

Geometry_dude

- 112

- 20

##

\gamma(t)= (x(t), y(t)) \, .

##

Taking the derivative with respect to time gives you the velocity $$\dot \gamma (t)$$. Getting rid of the parameter by solving y for x gives you the (image of the) curve without telling you how fast you go along that curve. Then differentiating ##y## with respect to ##x## tells you the slope of that curve at point ##(x, y(x))##. For simplicity I assumed there is only on ##y## value corresponding to a given ##x##-value.

- #6

chogg

- 129

- 10

His answer did not clear anything to me. You text-link is very big, gives to summarize?

From the top of the link:

Share:

- Last Post

- Replies
- 6

- Views
- 727

- Last Post

- Replies
- 9

- Views
- 1K

- Replies
- 37

- Views
- 1K

- Last Post

- Replies
- 1

- Views
- 826

- Last Post

- Replies
- 4

- Views
- 2K

- Replies
- 12

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 1K

- Last Post

- Replies
- 23

- Views
- 3K

- Replies
- 10

- Views
- 2K

- Replies
- 6

- Views
- 2K