5 Vector Field Proofs - apparently easy

[thomas49th]

Homework Statement

http://gyazo.com/94783c14f2d2d05e62e479ab33c73830

Homework Equations

I know the dot product and cross product, but even for the first one I don't see how either helps.

The Attempt at a Solution

1. the gradient of the 2 scalars multiplied together (not crossed or dotted just multiplied)
I know that the derivative of a scalar is a vector, but that won't help here

Can someone put me out of my misery?
Thomas

 

[vela]

The ith component of $\nabla(\phi\psi)$ is given by $\frac{\partial}{\partial x_i} (\phi\psi)$. That derivative is the regular old derivative you know and love, so what do you get when you apply the product rule?