1. Prove: If a polynomial p (x) is divisible by (x – a) 2 , then p ′(x) is divisible by (x – a). 2. Let f, g, and h be real-valued functions that are differentiable on an interval I. Prove that the...

1. Prove: If a polynomial p (x) is divisible by (x – a)², then p ′(x) is divisible by (x – a).

2. Let f, g, and h be real-valued functions that are differentiable on an interval I. Prove that the product function f g h : I →
 is differentiable on I and find ( f g h)′.

3. Let f : I → J, g : J → K, and h : K →
, where I, J, and K are intervals. Suppose that f is differentiable at c ∈ I, g is differentiable at f (c), and h is differentiable at g (f (c)). Prove that h o (g o f ) is differentiable at c and find the derivative