Basic Analysis I — Real Analysis · Problem 5.4.1

The Riemann Integral — Jiri Lebl

Mathematics — Real Analysis · exponential-logarithm

Problem

Given a real number

y

and

b > 0

, define

f : (0,\infty) \to \mathbb{R}

and

g : \mathbb{R} \to \mathbb{R}

f(x) := x^y

and

g(x) := b^x

. Show that

f

and

g

are differentiable and find their derivative.