Consider the surface $F(x,y,z)=x^3{z}^8+sin(y^3{z}^8)+4=0.$

Find the following partial derivatives

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}=\frac{-3x^2{z}^8}{(x^3(8z^7))+(cos(y^3{z}^8))(3y^2{z}^8)}$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}=$