Core Differentiation Rules
- Continuity Condition: $\lim_{x \to c^-} f(x) = \lim_{x \to c^+} f(x) = f(c)$
- Logarithmic Differentiation: Used for functions of the form $y = [u(x)]^{v(x)}$:
$$\ln y = v(x)\ln u(x) \implies \frac{1}{y}\frac{dy}{dx} = v'\ln u + \frac{v u'}{u}$$
