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- Thread starter Jhenrique
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- #2

lurflurf

Homework Helper

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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

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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

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differential in the inverse sense of integral, ie, "the differential of f wrt to x results the derivative of f"...Do you mean the derivative or the differential?

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

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

- #5

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##

\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

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

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