if V=ln(x^2 + y^2) show d^2V/dx^2 + d^2V/dy^2 = 0?

Question

any idea how to solve this? something to do with partial diffentiation. thx

Answer 1

dV/dx =1/(x^2+y^2) *2x

d^2V/dx^2 = 2/(x^2+y^2)^2 *( x^2+y^2-2x^2) = 2/(x^2+y^2)^2 *(y^2-x^2)
for
d^2V/dy^2 interchange x and y and get the result

Answer 2

♥ yes, partial! Just do it and see it = 0;