Common Derivatives

\begin{align*} \frac{d}{dx}[c] &= 0 &\text{Constant Rule} \\ \frac{d}{dx}[x] &= 1 \\ \frac{d}{dx}[x^n] &= nx^{n-1} &\text{Power Rule} \\ \frac{d}{dx}[cf(x)] &= c f'(x) &\text{Constant Multiple Rule} \\ \frac{d}{dx}[f(x) \pm g(x)] &= f'(x) \pm g'(x) &\text{Sum and Difference Rule} \\ \end{align*}

\begin{align*} \frac{d}{dx}[f(x)g(x)] &= f'(x)g(x) + f(x)g'(x) &\text{Product Rule} \\ \frac{d}{dx}\left[\frac{f(x)}{g(x)}\right] &= \frac{g(x)f'(x) - f(x)g'(x)}{[g(x)]^2} &\text{Quotient Rule} \\ \end{align*}

\begin{align*} \frac{d}{dx}[f(g(x))] &= f'(g(x))g'(x) &\text{Chain Rule} \\ \end{align*}

\begin{align*} \frac{d}{dx}[\sin(x)] &= \cos(x) \\ \frac{d}{dx}[\cos(x)] &= -\sin(x) \\ \frac{d}{dx}[\tan(x)] &= \sec^2(x) \\ \frac{d}{dx}[\csc(x)] &= -\csc(x)\cot(x) \\ \frac{d}{dx}[\sec(x)] &= \sec(x)\tan(x) \\ \frac{d}{dx}[\cot(x)] &= -\csc^2(x) \\ \end{align*}

\begin{align*} \frac{d}{dx}[e^x] &= e^x \\ \frac{d}{dx}[a^x] &= a^x \ln(a) \\ \frac{d}{dx}[\ln(x)] &= \frac{1}{x} \\ \frac{d}{dx}[\log_a(x)] &= \frac{1}{x \ln(a)} \\ \end{align*}