Find the derivative of (delw)/(dely) of (1)/(w^(6)+x^(6))+(1)/(w^(6)+y^(6))=(1)/((5)^((6))+(5)^((6)))+(1)/((5)^((6))+(5)^((6))) at (x,y,w)=(5,5,5) using implicit differentiation. Use symbolic notation. Which of the following options is the correct derivative?

A. (delw)/(dely) = (6w^5)/(w^6 + x^6) + (6w^5)/(w^6 + y^6)
B. (delw)/(dely) = (6w^5)/(w^6 + x^6) + (6w^5)/(w^6 + y^6) + (6w^5)/(w^6 + 5^6) + (6w^5)/(w^6 + 5^6)
C. (delw)/(dely) = (6w^5)/(w^6 + x^6) + (6w^5)/(w^6 + y^6) + (6w^5)/(5^6 + 5^6) + (6w^5)/(5^6 + 5^6)
D. (delw)/(dely) = (6w^5)/(w^6 + x^6) + (6w^5)/(w^6 + y^6) + (6w^5)/(5^6 + 5^6) + (6w^5)/(5^6 + 5^6)