## Thomas' Calculus 13th Edition

$\nabla g(x,y,z)=(y+z) i +(x+z) j +(y+x) k$
Re-write as: $g(x,y,z)=xy+yz+xz$ The gradient field of $f(x,y,z)$ can be computed as: $\nabla f(x,y,z) =\dfrac{\partial (f(x,y,z))}{\partial x} i+\dfrac{\partial (f(x,y,z))}{\partial y} j+\dfrac{\partial (f(x,y,z))}{\partial z}k$ Thus, the gradient is: $\nabla g(x,y,z)=(y+z) i +(x+z) j +(y+x) k$