How did we get to the constant in r\frac{\partial p}{\partial r}=c_1?

In summary, we used the fact that the derivative of an expression is zero to show that the expression must be a constant, and then we integrated to solve for the constant.
  • #1
An1MuS
38
0
Hi,

When we have [tex]\frac{\partial}{\partial r}(r\frac{\partial p}{\partial r})=0[/tex]

and we get

[tex]r\frac{\partial p}{\partial r}=c_1[/tex]

To get there, did we do this

[tex]\int\frac{\partial}{\partial r}(r\frac{\partial p}{\partial r}) dr=\int 0 dr[/tex]

or

[tex]\partial (r\frac{\partial p}{\partial r})=0\partial r[/tex]
[tex]\int \partial (r\frac{\partial p}{\partial r})=\int 0\partial r[/tex]

and why?

Thanks in advance
 
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  • #2
Well, yes, but you could also think of it this way: This
[tex]
\frac{\partial}{\partial r} \left(r \frac{\partial p}{\partial r} \right) = 0
[/tex]

tells you that the derivative wrt [tex] r [/tex] of the expression inside parentheses is zero, so that expression must be a constant.
 

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