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$\frac{d}{dx}(c) = 0$

$\frac{d}{dx}(x^n) = nx^{n-1}$

$\int c\,dx = cx + C$

$\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$

$\int e^x\,dx = e^x + C$

$\int \frac{1}{x}\,dx = \ln|x| + C$

$\int \sin(x)\,dx = -\cos(x) + C$

$\int \cos(x)\,dx = \sin(x) + C$

$\int \tan(x)\,dx = -\ln|\cos(x)| + C$

$\int_a^b f'(x)\,dx = f(b) - f(a)$

$\frac{d}{dx}\int_a^x f(t)\,dt = f(x)$

$\lim_{x \to \infty} \frac{f(x)}{g(x)} = 0$ if $\deg(f) < \deg(g)$

$\frac{d}{dx}(uv) = u'v + uv'$

$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$

$\text{Area} = \int_a^b f(x)\,dx$

$\text{Volume} = \pi \int_a^b [f(x)]^2\,dx$

$\frac{d}{dx}\arcsin(x) = \frac{1}{\sqrt{1-x^2}}$

$\frac{d}{dx}\arccos(x) = -\frac{1}{\sqrt{1-x^2}}$

$\frac{d}{dx}\arctan(x) = \frac{1}{1+x^2}$

$\text{Slope} = f'(x)$

$[f^{-1}(x)]' = \frac{1}{f'[f^{-1}(x)]}$

$\int u dv = uv - \int v du$

$\frac{d}{dx}\sec(x) = \sec(x)\tan(x)$

$\frac{d}{dx}\left(\frac{u}{v}\right) = \frac{u'v - uv'}{v^2}$

$\frac{d}{dx}\csc(x) = -\csc(x)\cot(x)$

$\frac{d}{dx}\arcsec(x) = \frac{1}{|x|\sqrt{x^2 - 1}}$

$\frac{d}{dx}\arccsc(x) = -\frac{1}{|x|\sqrt{x^2 - 1}}$

$\frac{d}{dx}\cosh(x) = \sinh(x)$

$\frac{d}{dx}\sinh(x) = \cosh(x)$

$\int \sec^2(x)\,dx = \tan(x) + C$

$\int \csc^2(x)\,dx = -\cot(x) + C$

$f^{-1}(y) = x \iff f(x) = y$

$f(c)(b-a) = \int_a^b f(x)\,dx$ where $a \leq c \leq b$

$\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$

$\frac{d}{dx}e^x = e^x$

$\frac{d}{dx}\log_a(x) = \frac{1}{x\ln(a)}$

$\frac{d}{dx}\sin(x) = \cos(x)$

$\frac{d}{dx}\cos(x) = -\sin(x)$