Question

Determine the gradient of a function φ = x^4 +y^2 +z^3 at the point (1,-2,-1)

Answer 1

The gradient is

$$\nabla\phi=\dfrac{\partial }{\partial x}x^4\textbf i+\dfrac{\partial }{\partial y}y^2\textbf j+\dfrac{\partial }{\partial z}z^3\textbf k,\\\space\\ \nabla\phi=4x^3\textbf i+2y\textbf j+3z^2\textbf k,\\\space\\ \nabla\phi=4\textbf i-4\textbf j+3\textbf k.$$