Formulari d'anàlisi

$(x^n)' = n\,x^{n-1}$

$(\sqrt{u})' = \dfrac{u'}{2\sqrt{u}}$

$(e^u)' = e^u \cdot u'$

$(a^u)' = a^u \ln a \cdot u'$

$(\ln u)' = \dfrac{u'}{u}$

$(\sin u)' = \cos u \cdot u'$

$(\cos u)' = -\sin u \cdot u'$

$(\tan u)' = \dfrac{u'}{\cos^2 u}$

$(\arctan u)' = \dfrac{u'}{1+u^2}$

$(u+v)' = u' + v'$

$(u \cdot v)' = u'v + uv'$

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

$[f(g(x))]' = f'(g(x)) \cdot g'(x)$

$f'(a) = \lim_{h \to 0} \dfrac{f(a+h)-f(a)}{h}$

$y - f(a) = f'(a)(x-a)$

$f' > 0 \text{ creix}, \ f' < 0 \text{ decreix}$

$f'(x) = 0$

$f''(x) < 0$

$f''(x) > 0$

$f''(x) = 0 \text{ i canvia de signe}$

$\lim \dfrac{f}{g} = \lim \dfrac{f'}{g'} \ \text{(només amb } \tfrac{0}{0} \text{ o } \tfrac{\infty}{\infty})$

$\int x^n dx = \dfrac{x^{n+1}}{n+1} + C \quad (n \neq -1)$

$\int \dfrac{u'}{u} dx = \ln|u| + C$

$\int e^{kx} dx = \dfrac{e^{kx}}{k} + C$

$\int \sin(kx)\,dx = -\dfrac{\cos(kx)}{k} + C$

$\int \cos(kx)\,dx = \dfrac{\sin(kx)}{k} + C$

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

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

$A = \int_a^b |f(x) - g(x)|\,dx$

$V = \pi\int_a^b [f(x)]^2 dx$

$\lim_{x\to\infty} \dfrac{ax^n}{bx^n} = \dfrac{a}{b}$

$\pm\infty$

$0$

factoritza i simplifica

$\lim_{x\to\infty}\left(1+\dfrac{1}{x}\right)^x = e$

$\lim_{x\to a^-} f = \lim_{x\to a^+} f = f(a)$