Find second partial derivatives Zxx Zxy Zyx and Zyy for z

Find second partial derivatives (Zxx, Zxy = Zyx, and Zyy) for z = (X^2 + y^2)^10. Please show steps as I have the correct answer. Thanks!

z=(x^2+y^2)^10

Z_x=10*(x^2+y^2)^9 *(2*x)=20*x*((x^2+y^2)^9)

Z_y=10*(x^2+y^2)^9 *(2*y)=20*y*((x^2+y^2)^9)

Z_xx=20*x*9*(x^2+y^2)^8 *(2*x)=360*x²*((x^2+y^2)^8)

Z_xy=20*x*((x^2+y^2)^8)*9*2*y=360*x*y*((x^2+y^2)^8)

Z_yy=20*y*((x^2+y^2)^8)*9*2*y=360*y²*((x^2+y^2)^8)