Chapter 15.1, Problem 24E

To determine

The conservative vector field for the givenpotential function f(x, y, z) = $\sqrt{x^{{}^2}y+z^2}$ by evaluating its gradient.

lution: The conservative vector field for the given potential function f(x, y, z) = $\sqrt{x^{{}^2}y+z^2}$ is given

by F (x, y, z) = $\&\#8711;\nabla \langle \text{em}\rangle f\langle /\text{em}\rangle =$ $\frac{xy}{\sqrt{x^{{}^2}y+z^2}}\widehat{i}+\frac{x^2}{2\sqrt{x^{{}^2}y+z^2}}\widehat{j}+\frac{z}{\sqrt{x^{{}^2}y+z^2}}\widehat{k}$.