If f is a scalar field and f, g are vector fields, then f f, f · g, and f × g are defined by the following.(f f)(x, y, z) = f(x, y, z) f(x, y, z)(f · g)(x, y, z) = f(x, y, z) · g(x, y, z)(f × g)(x, y, z) = f(x, y, z) × g(x, y, z) find an identical expression, assuming that the appropriate partial derivatives exist and are continuous.

a. curl(f f)f div f + f · ∇f
b. grad(div f) − ∇2f f
c. curl f + (∇f) × ff d
d. f + (∇f) × f
e. none of above