For the vectorial field F A Find the divergence for F B Fin

For the vectorial field F A ) Find the divergence for F B) Find the rotational of F

Para el campo vecorial F (x, y, z) = (x2 + sinyz)i + (y - xe-z)j + z2k Encuentre la divergencia de F Encuentre el rotacional de F

Solution

1) the divergence of a vectorial field is defined as div F = F\'_xi+ F\'_yj +F\'_zk (partial derivatives)

Fx = x^2 + sin(yz) ----> F\'x = 2x

Fy = y - xe^-z -----> F\'y = 1

Fz = z²k -----------> F\'z = 2z

Finally div F = 2xi + j + 2zk

2) Curl F is defined as: curl F = - xe^-zi + ycos(yz) j - (e^-z + zcos(yz))k