Some Foundation Math Concepts for Quantitative Finance The chain rule: $$ \frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x) $$ The product rule: $$ \frac{d}{dx} [f(x)g(x)] = f'(x)g(x) + f(x)g'(x) $$ General Taylor series $$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n $$