Basic Analysis I — Real Analysis · Problem 4.1.1

The Derivative — Jiri Lebl

Mathematics — Real Analysis · derivative-product-rule

Problem

Prove the product rule. Hint: Prove and use f(x)g(x)−f(c)g(c)=f(x)(g(x)−g(c))+(f(x)−f(c))g(c)f(x)g(x) - f(c)g(c) = f(x)\bigl(g(x) - g(c)\bigr) + \bigl(f(x) - f(c)\bigr)g(c).

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