Consider the given vector field. F(x, y, z) =[7e^xy sin(z) j ]+[ 8y tan^−1(x/z) k] Find the curl of the vector field and the divergence?

div(F) = d(F_y)/dy + d(F_z)/dz.
Is that e^(xy)? The parentheses are necessary !!!
Anyway, so d(F_y)/dy would then be
7xe^(xy) sin(z),
and d(F_z)/dz would be
8y [1/(1 + x^2/z^2)] * (-x/z^2)
= -8xy/(z^2 + x^2).
So the div(F) is 7xe^(xy) sin(z) - 8xy/(z^2 + x^2).

curl(F) = k*[d(F_y)/dx - d(F_x)/dy]
+ i*[d(F_z)/dy - d(F_y)/dz]
+ j*[d(F_x)/dz - d(F_z)/dx].
These will not be really hard to figure out, just tedious !!!