Partial derivatives, equation help

[tweety1234]

Homework Statement

Heat is being conducted radially through a cylindrical pipe. The temperature at a radius r is T(r). In Cartesian co-ordinates, r = \sqrt{(x^{2}+ y^{2}})

show that \frac{\partial T}{\partial x} = \frac{x}{r} \frac{dT}{dr}

 

[madah12]

cant you just say \frac{\partial T}{\partial x} = \frac{\partial T}{\partial r} * \frac{\partial r}{\partial x}
but since T is function of r you can write \frac{\partial T}{\partial r} as dT/dr I am not sure this is correct though.

 

[tweety1234]

cant you just say \frac{\partial T}{\partial x} = \frac{\partial T}{\partial r} * \frac{\partial r}{\partial x}
but since T is function of r you can write \frac{\partial T}{\partial r} as dT/dr I am not sure this is correct though.

oh I thought we might have to make use of the equation relating x and r given in the question ?

 

[madah12]

yes to get the partial of r with respect to x you need the equation right?

 

[tweety1234]

But the expression wants x/r?

 

[madah12]

I think that the <br /> \frac{\partial T}{\partial r} <br /> will give you the x/r part