Notes for Math 220, Calculus 2

\begin{align*} \frac{d}{dx}(k f(x)) \amp= k \frac{df}{dx}\\ \frac{d}{dx}(f(x) \pm g(x)) \amp= \frac{df}{dx} \pm \frac{dg}{dx} \end{align*}

\begin{align*} \frac{d}{dx}(f(x)g(x)) \amp= \frac{df}{dx} g(x) + f(x) \frac{dg}{dx}\\ \frac{d}{dx}(f(x)/g(x)) \amp= \frac{\ds \frac{df}{dx} g(x) - f(x) \frac{dg}{dx}}{g^2(x)}\\ \frac{d}{dx} (f(g(x)) \amp= f'(g(x))\frac{dg}{dx}\\ \text{That is, with } u = g(x), y = f(u),\\ \frac{dy}{dx} \amp = \frac{dy}{du}\frac{du}{dx} \end{align*}