Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates,

show that

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- Dec 13th 2010, 02:34 PMTweetyPartial derivatives, word problem help
Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates,

show that - Dec 13th 2010, 02:45 PMadkinsjr

You have to differentiate r with restpect to x, this is just .

So - Dec 13th 2010, 02:53 PMTweety
Thank you so much, but I dont understand what the first expression is and how you got it?

your saying ?

How comes?

Also for , you took the partial derivative of r with respect to x, from the equation ?

so you get this expression ;

but how does that equal the expression; ?

thank you. - Dec 13th 2010, 02:55 PMTweety
edit; I actually understand how you got the first expression, thanks, could please explain the rest?

Thank you - Dec 13th 2010, 03:08 PMadkinsjrQuote:

Thank you so much, but I dont understand what the first expression is and how you got it?

your saying ?

How comes?

Quote:

Also for , you took the partial derivative of r with respect to x, from the equation ?

so you get this expression ;

but how does that equal the expression; ?

thank you.

The derivative of a function like is .

You have to apply the chain rule to find the partial of r with respect to x.

Remember that so just substitute that into the partial derivative for r with respect to x, and you get - Dec 13th 2010, 03:33 PMTweety
Thank you , I understand your method now.

- Dec 13th 2010, 03:53 PMTweety
sorry just one question, how does come into the equation ? It seems like its just been put there?

Thank you