Exercise 591Calculus › Multivariable calculus › Vector calculusL1Added 3 Nov 2026

The divergence

#divergence#vector field#computation

Statement

Compute $\operatorname{div}\vec F$ for $\vec F=(x^2y,\,xy^2,\,z^3)$ .

Hint

$\operatorname{div}\vec F=\partial_xP+\partial_yQ+\partial_zR$ .

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Compute. $\partial_x(x^2y)=2xy$ , $\partial_y(xy^2)=2xy$ , $\partial_z(z^3)=3z^2$ .

Divergence. $\operatorname{div}\vec F=2xy+2xy+3z^2=4xy+3z^2$ .

Conclusion. $\operatorname{div}\vec F=4xy+3z^2$ .