Suppose that the functions and g are defined throughout an open interval containing the point x 0 , that is differentiable at x

Suppose that the functions ƒ and g are defined throughout an open interval containing the point x₀, that ƒ is differentiable at x₀, that ƒ(x₀) = 0, and that g is continuous at x₀. Show that the product ƒg is differentiable at x₀. This process shows, for example, that although|x| is not differentiable at x = 0, the product x |x | is differentiable at x = 0.