【Calculus & Algebra】Limits & Derivatives
Basics of Derivatives Derivative: Let $y=f(x)$, then $$f'(x) = \frac{dy}{dx} = lim_{\Delta x \to 0} \frac{f(x+\Delta x) - f(x)}{\Delta x}$$ The Product Rule: If $u=u(x)$ and v=v(x) and their respective derivatives exist, $$\frac{d(uv)}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}, (uv)' = u'v + uv'$$ The quotient rule: $$\frac{d}{dx}(\frac{u}{v}) = \cfrac{(v\frac{du}{dx}-u \frac{dv}{dx})}{v^2}, (\fra..
