I'm looking for the indicated second-order partial derivative for the function f(x,y).

f(x,y)=(1+2xy^2)^8

What I have is:

fx=(2y^2)^8 fy=(4xy)^8

fxx=0 fyy=(4x)^8

fxy=(4y)^8 fyx=4^8

I'm not good at the language of math so I'm not sure if I need to go on and if so, if I have even done what I have right. Any help is more than appreciated.