The divergence of the vector field { }^{i-e^{x}(\cos y \hat{i}-\sin y^{2})} is

GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

Question : 15 of 65

Marks: +1, -0

The divergence of the vector field

{ }^{i-e^{x}(\cos y {i}↖{∧}-\sin y^{2})}

Solution:

{u}↖{→}=e^{x} \cos y i+e^{x} ⋅ \sin y j

∇ ⋅ {u}↖{→}=\;{∂}/{∂ x}(u_{1})+\;{∂}/{∂ y}(u_{2})

=\;{∂}/{∂ x}(e^{x} ⋅ \cos y)+\;{∂}/{∂ y}(e^{x} ⋅ \sin y)

=e^{x} \cos y+e^{x} \cos y

∇ ⋅ \ov{u}=2 e^{x}, \cos y

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