(Continuation of Exercise 21.) Use the result of Exercise 21 to show that the following...

(Continuation of Exercise 21.) Use the result of Exercise 21 to show that the following functions are differentiable at x = 0.

21. Suppose that the functions ƒ and g are defined throughout an open interval containing the point x₀, that ƒ is differentiable at x_0, that f(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.