a) Prove that if q = n/m for n Z and m N, then for every x, a (0, ). b) [POWER

a) Prove that if q = n/m for n ˆŠ Z and m ˆŠ N, then

for every x, a ˆŠ (0, ˆž).
b) [POWER RULE] Use Exercise 4.1.2 and part a) to prove that xq is differentiable on (0, ˆž) for every q ˆŠ Q and that (xq)' = qxq-1.

x" - a" = (x - a")(x(m-1) +xg(m-2)a +..+ xa m-2) + a9(m-1)