Let $\vec{F}=\left(4 x^{3}-y^{6} \sin x\right) \vec{i}+\left(6 y^{5} \cos x+4 z\right) \vec{j}+4 y \vec{k}$

Essay

Let $\vec{F}=\left(4 x^{3}-y^{6} \sin x\right) \vec{i}+\left(6 y^{5} \cos x+4 z\right) \vec{j}+4 y \vec{k}$ Show that $\vec{F}$ is a gradient field by finding its potential function.