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
$$
\frac{d}{dx}\left[ \frac{f(x)}{g(x)} \right] = \frac{g(x)f'(x) – f(x) g'(x)}{[g(x)]^2}.
$$

E 3.3 Exercises