Question

Evaluate ∇2U, given that Ux,y,z=xy2z3

Select one:

A. y2z3+2xz3+6xy2z

B. x2y2z+2xz3-6xy2z

C. y2z3+2xyz3+3xy2z2

D. 2xz3+6xy2z

Answer 1

$U\left( x,y,z \right) =xy^2z^3\\\nabla ^2U\left( x,y,z \right) =\frac{\partial ^2U}{\partial x^2}+\frac{\partial ^2U}{\partial y^2}+\frac{\partial ^2U}{\partial z^2}=\\=0+2xz^3+6xy^2z=2xz^3+6xy^2z\\D\,\,is\,\,correct$