Basic Analysis I — Real Analysis · Problem 4.4.3

The Derivative — Jiri Lebl

Mathematics — Real Analysis · negative-nth-root

Problem

Let

n \in \mathbb{N}

be even. Prove that every

x > 0

has a unique negative

n

th root. That is, there exists a negative number

y

such that

y^n = x

. Compute the derivative of the function

g(x) \mathrel{\mathop:}= y