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.

Question

Quizplus · Accepted Answer

The Answer of 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.

Let F⃗=(4x3−y6sin⁡x)i⃗+(6y5cos⁡x+4z)j⃗+4yk⃗\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}F=(4x3−y6sinx)i+(6y5cosx+4z)j​+4yk

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