Seja ƒ = ℝ3 → ℝ dada por ƒ(x,y,z) = x sen(yz) + zexy. O gradiente de ƒ é:
⊽ƒ(x,y,z) = (cos(yz) + yzexy)i + (xz cos(yz) + xzexy)j + (xy cos(yz) + exy)k.
⊽ƒ(x,y,z) = (cos(yz) + zexy)i + (xz cos(yz) + zexy)j + (xy cos(yz) + exy)k.
⊽ƒ (x,y,z) = (sen(yz) + yzexy)i + (xz cos(yz) + xzexy)j + (xy cos(yz) + exy)k.
⊽ƒ (x,y,z) = (sen(yz) + zexy)i + (xz cos(yz) + zexy)j + (xy cos(yz) + exy)k.