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Question: Algebra-like manipulations of derivatives

Question:Algebra-like manipulations of derivatives

lsitongia 16
derivative student
April 07 2010
0
Sometimes I've seen manipulations like this:

dx/dt = dx/dy dy/dt

in which the symbols of the derivatives are multiplied and cancelled like terms in equations. I can't remember nor find the justification for doing this. What's the explanation?

I can't get Maple to do this for me. If I make x an expression of y and y an expression of t, then it substitutes the expressions into the arguments, and I get a nonsensical result:

> y := t^3;
3
t
> x := 'y^2';
2
y
> diff(x, t);
5
6 t
> diff(y, t);
2
3 t
> diff*(x, y);
/ 6 3\
diff \t , t /
> (diff(y, t))*diff*(x, y);
2 / 6 3\
3 t diff \t , t /

Is this sort of manipulation always reasonable and how can I do it in Maple?

Thanks,
==Leonard


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