Originally Posted by alex34 " What force vector corresponds to a potential energy U=3x^2+5xy+z^2 ?"
By taking the derivative with respect to xyz in each I end with F = (6x+5y)i + (5x)j + (2z)k 
Yes, the force corresponding to a given potential energy is its "gradient".
Then I am asked to determine the power if the velocity it moves with is v = (x+2yz)j
I know power = FdotV
so.. (6x+5y)i multiplied by 0 = 0
(5x)j multipled by (x+2yz)j = 5 + 0 + 0 = 5 < This is what i am unsure about. Dotting two vectors with multiple variables. Please let me know if I did or didnt do it correctly. Thank you.

Yes, with v having 0 x and z components, the dot product of F with v is ((5x)(x+ 2y z)= 5x^2+ 10xy 5xz. That depends on the values of x, y, and z. Where did you get "5+ 0+ 0"?