Answer
$div (F+G)=div F+div G$
Work Step by Step
Need to prove that $div (F+G)=div F+div G$
Let us consider that $F=A i+B j+C k$
$div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}$
Suppose $F=ai+bj; G=ci+dj$
and $div (F+G)=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial x}+\dfrac{\partial d}{\partial y}$
or, $div (F+G)=div F+div G$
Hence, $div (F+G)=div F+div G$
