Gradient of a scalar field, divergence and rotational of a vector field

Calculate the divergence and the rotational of the following vector function: $$F(x,y,z)=(4\cdot x^3 \cdot y-z, y^3, \cos z \cdot 4 \cdot x )$$

$$\displaystyle div(F)=\frac{\partial}{\partial x}(4\cdot x^3 \cdot y-z)+\frac{\partial}{\partial y}(y^3)+\frac{\partial}{\partial z}(\cos z \cdot 4 \cdot x)=$$ $$=12\cdot y\cdot x^2+3\cdot y^2-4\cdot x\cdot \sin z$$

$$\displaystyle rot (F)=\Bigg(\frac{\partial}{\partial y}(\cos z \cdot 4 \cdot x)-\frac{\partial}{\partial z}(y^3),\frac{\partial}{\partial z}(4\cdot x^3 \cdot y-z)-\frac{\partial}{\partial x}(\cos z \cdot 4 \cdot x),$$ $$\displaystyle ,\frac{\partial}{\partial x}(y^3)-\frac{\partial}{\partial y}(4\cdot x^3 \cdot y-z) \Bigg)=\Big( 0-0,-1-4\cos z, 4 \cdot x^3 \Big)$$

$$div(F)=12\cdot y\cdot x^2+3\cdot y^2-4\cdot x\cdot \sin z$$

$rot(F)=\Big(0,-1-4\cos z, 4 \cdot x^3 \Big)$

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