# Partial using the chain rule

1. Sep 25, 2008

### Somefantastik

$$u^{*}(r^{*},\theta^{*},\phi^{*}) = \frac{a}{r^{*}}u(\frac{a^{2}}{r^{*}},\theta^{*},\phi^{*})$$

$$\frac{\partial u^{*}}{\partial r^{*}}= \frac{a}{r^{*}}u_{r^{*}} \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right) \left( -\frac{a^{2}}{r^{2*}} \right) - \frac{a}{r^{*2}} u \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right)$$

where $$u_{r^{*}}$$ is the partial of u w.r.t r*

Did I do this right? Is there a better way of representing $$u_{r^{*}} \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right)$$

Last edited: Sep 25, 2008
2. Sep 25, 2008

### smallphi

Calculation is right but pedantically speaking you mean derivative of u with respect to its first argument which is a^2/r* not r*.

I don't know what kind of notations mathematicians use for that, symbolic programs like Mathematica would denote it like Derivative[1,0,0].

3. Sep 25, 2008

### Somefantastik

well I'm trying to crank out the laplacian in spherical to show it u* is harmonic. So I'm just trying to differentiate with respect to each component and sub it into the laplacian in spherical and HOPEFULLY get zero.

4. Sep 28, 2008

### Somefantastik

I still need help with this. Is there anybody out there who can help me?