Functions that are composed of other differentiable functions can be differentiated using systematic rules. For differentiable functions $f(x)$ and $g(x)$ and a constant $C$, the primary rules are:

• Constant multiple rule: $\frac{d}{dx} [C f(x)] = C \frac{d}{dx} f(x)$
• Sum rule: $\frac{d}{dx} [f(x) + g(x)] = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)$
• Product rule: $\frac{d}{dx} [f(x) g(x)] = f(x) \frac{d}{dx} g(x) + g(x) \frac{d}{dx} f(x)$
• Quotient rule: $\frac{d}{dx} \frac{f(x)}{g(x)} = \frac{g(x) \frac{d}{dx} f(x) - f(x) \frac{d}{dx} g(x)}{g^2(x)}$