For polar coordinates, ##u(x,y)=u(r,\theta)##. Using Chain Rule:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\partial u}{\partial x}=\frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta}\frac{\partial \theta}{\partial x}[/tex]

The book gave

[tex]\frac{\partial ^2 u}{\partial x^2}=\frac{\partial }{\partial x}\left(\frac{\partial u}{\partial x}\right)=\frac{\partial }{\partial r}\left( \frac{\partial u}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial u}{\partial \theta}\frac{\partial \theta}{\partial x}\right)[/tex]

But should it be like this according to the first equation using Chain Rule? That it has to include the ##\theta## part?:

[tex]\frac{\partial ^2 u}{\partial x^2}=\frac{\partial }{\partial r}\left(\frac{\partial u}{\partial x}\right)\frac{\partial r}{\partial x}+\frac{\partial }{\partial \theta}\left(\frac{\partial u}{\partial x}\right)\frac{\partial \theta}{\partial x}[/tex]

I just follow the form like the first equation. If I am wrong, can you explain why?

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question in Partial differential equation.

**Physics Forums | Science Articles, Homework Help, Discussion**