Solve the below:
Q: Prove the following product rule for vector derivatives given the functions:
vec{A} = 2x x-hat + y y-hat + 4z z-hat
and
vec{B} = 2y x-hat - 3x y-hat
for the following product rule:
Del(A.B) [Gradient of A.B] = A X (curl B) + B X (curl A) + (A.Del)B + (B.Del)A
where I denoted the gradient as Del.