Problems from 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)=(4x3yz,y3,cosz4x)

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Development:

div(F)=x(4x3yz)+y(y3)+z(cosz4x)= =12yx2+3y24xsinz

rot(F)=(y(cosz4x)z(y3),z(4x3yz)x(cosz4x), ,x(y3)y(4x3yz))=(00,14cosz,4x3)

Solution:

div(F)=12yx2+3y24xsinz

rot(F)=(0,14cosz,4x3)

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