8. Let I be an open interval, let a E I, and let I, g be functions from I to R.

(a) Prove that if 1 and g are differentiable at

a, then 1 + g is differentiable at a with

(f + g)'

(a) = f'

(a) + g'(a).

(b) Prove that if 1 is differentiable at a and a E R, al is differentiable at a with

(al)'

(a) = af'(a).