Assume that function h  (  h(x)  ) is the product of two functions --  f(x) and g(x). If f(x) and g(x) are both differentiable at x, then their product h(x) will be differentiable at x as well. And the derivative of h(x) can be interpreted as the following formula:

h'(x)=[f(x)g(x)]'=f'(x)g(x)+f(x)g'(x)

And this is the formula of Power Rule.