Answer to Question #227514 in Calculus for Unknown346307

Question

2. Prove that ∇ · (A ~ + B~ ) = ∇A~ + ∇B~

Answer 1

 ∇ · (A ~ + B~ ) = ∇A~ + ∇B~

∇ · (A ~ + B~ )

For example from distributive g(a+b)= ga+gb

Distributive law, in mathematics, the law is related to the operations which involve multiplication and addition, stated symbolically, g(a + b) = ga+ gb; that is, the monomial factor  g is distributed, or separately applied, to each term of the binomial factor a + b, resulting in the product ga+ gb.

From distributive law it is easy and clear to know that the result of first adding several numbers and then multiplying the sum by some number is the same as first multiplying each separately by the number and then adding the products. 

Hence let

∇ ....... g

A~..........a

B~...........b

Hence [ga+gb] = ∇A~ + ∇B~

Hence shown