Question

Problem 3 Determine the gradient of the scalar field, and verify with MATLAB

Answer 1

We are given $f(x.y,z)=3x^{2}y+yxz-2z^{2}xy^{3}$ . Now the gradient of the function =$\vec{\triangledown }f=\frac{\partial }{\partial x}f\vec{i}+\frac{\partial }{\partial y}f\vec{j}+\frac{\partial }{\partial z}f\vec{k}=(6xy+yz-2z^{2}y^{3})\vec{i}+(3x^{2}+xz-6z^{2}xy^{2})\vec{j}+(xy-4xy^{3}z)\vec{k}$.