Find the curl of vector field.
F(x, y, z) = xy i + yz j + xy k
∇xF = x^2 • z i + y^2•x j + z^2 k
The book's answer is
∇xF = -y i - z j - x k
Who is right and why?
The book's answer is correct. I can't imagine how you got your answer! Your answer has polynomials of higher power than the original vector while differentiating always reduces the power of a polynomial.
$\displaystyle \nabla\times F= \left|\begin{array}{ccc} \vec{i} & \vec{j} & \vec{k} \\ \frac{\partial F}{\partial x} & \frac{\partial F}{\partial y} & \frac{\partial F}{\partial z} \\ xy & yz & xz \end{array}\right|= (0- x)\vec{i}-(z- 0)\vec{j}+ (0- x)\vec{k}= -x\vec{i}- \vec{j}- \vec{k}$.