Homework Help: Calculus-differentiation Help Please

thenewbosco · Sep 25, 2005

calculus--differentiation Help Please!!!

if [tex]x=\rho cos \theta[/tex] and [tex] y=\rho sin \theta[/tex]

prove that if U is a twice differentiable function of x and y that
[tex]\frac{\partial^2U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2} = \frac{\partial^2 U}{\partial \rho^2} + \frac{1}{\rho}\frac{\partial U}{\partial \rho} + \frac{1}{\rho^2}\frac{\partial^2 U}{\partial \theta^2}[/tex]

I have absolutely no clue how to get started on this one.

thanks

thenewbosco · Sep 25, 2005

anyone...........

Tzar · Sep 25, 2005

Try using the chain rule to find [tex]\frac{\partial U}{\partial\theta} [/tex]. The do it agian to find the second derivatives. Hope it works!

thenewbosco · Sep 25, 2005

I could try this except for the fact that i do not know what U equals...is there some assumption i am supposed to make here

Tzar · Sep 25, 2005

No assumption. Just use [tex]\frac{\partial U}{\partial \theta } = \frac{\partial U}{\partial x} \frac{\partial x}{\partial \theta}+ \frac{\partial U}{\partial y} \frac{\partial y}{\partial \theta}[/tex]

Tzar · Sep 25, 2005

its messy!

thenewbosco · Sep 25, 2005

i'm sorry i don't quite understand what i am supposed to be doing here. can i get a some explanation as to how and why to start this. i have really no idea here. thanks