More Properties of Derivatives: If \(f(x)\) and \(g(x)\) are differentiable at \(x\), then

• Product Rule:
  $$\frac{d}{dx}[f(x) \cdot g(x)] = \frac{d}{dx}[f(x)] \cdot g(x) + \frac{d}{dx}[g(x)] \cdot f(x) $$
• Quotient Rule:
  $$\frac{d}{dx}\left[ \frac{f(x)}{g(x)}\right] = \frac{g(x) \cdot\frac{d}{dx}[f(x)] – \frac{d}{dx}[g(x)] \cdot f(x)}{(g(x))^2}$$