Understanding the Chain Rule for Partial Derivatives in Multivariable Calculus

[Somefantastik]

[tex] u^{*}(r^{*},\theta^{*},\phi^{*}) = \frac{a}{r^{*}}u(\frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}) [/tex]

[tex] \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) [/tex]

where [tex] u_{r^{*}} [/tex] is the partial of u w.r.t r*

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

 

[smallphi]

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

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].

 

[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.

 

[Somefantastik]

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