# 3.3 | Product and Quotient Rules and Higher-Order Derivatives

The Product Rule: Suppose $$f$$ and $$g$$ are differentiable functions at $$x$$, then $$f \cdot g$$ is differentiable at $$x$$ and
$$\frac{d}{dx}[f(x) \cdot g(x)] = f(x) g'(x) + g(x) f'(x).$$
The Quotient Rule: Suppose $$f$$ and $$g$$ are differentiable functions at $$x$$, then $$f/g$$ is differentiable at $$x$$, provided $$g(x) \not = 0$$, and
$$\frac{d}{dx}\left[ \frac{f(x)}{g(x)} \right] = \frac{g(x)f'(x) – f(x) g'(x)}{[g(x)]^2}.$$