Use the definitions listed $in$ Section $6\mathrm{.}1\mathrm{.}2$ with $f(x,y,z)=x^2+yz,$vec$(F)(x,y,z)=($:$xy,yz,xz$:$),$ and vec$(G)(x,y,z)=($:$-sin(z),e^{xz},y$:$).$

Compute the vector $(f(vec(F)+$vec for vectors.