matematicas

Aquí están las principales funciones primitivas:

Función $F \,\!$ : primitiva de $f \,\!$	función $f \,\!$ : derivada de $F \,\!$
$f\left(x\right) = \frac {x^{n+1}}{n+1} + k \,\!$	$\begin{matrix}f'\left(x\right) = x^n & & \mathrm{ , para} & n \neq -1 \end{matrix} \,\!$
$f\left(x\right) = e^x + k \,\!$	$f'\left(x\right) = e^x \,\!$
$f\left(x\right) = \ln\left(x\right) + k \,\!$	$f'\left(x\right) = \frac{1}{x} \,\!$
$f\left(x\right) = \frac {x^{1-n}}{1-n} + k \,\!$	$\begin{matrix}f'\left(x\right) = \frac {1}{x^n} & & \mathrm{ , para} & n \neq 1 \end{matrix} \,\!$
$f\left(x\right) = -\cos\left(x\right) + k \,\!$	$f'\left(x\right) = \sin\left(x\right) \,\!$
$f\left(x\right) = \sin\left(x\right) + k \,\!$	$f'\left(x\right) = \cos\left(x\right) \,\!$
$f\left(x\right) = \tan\left(x\right) + k \,\!$	$f'\left(x\right) = \frac {1}{\cos^2\left (x\right)} \,\!$
$\begin{matrix}f\left(x\right) = \frac {a^x}{\ln(a)} + k & & \mathrm{, si} & a > 0 \end{matrix} \,\!$	$f'\left(x\right) = a^x \,\!$
$f\left(x\right) = \frac {2}{3} \sqrt{x}^3 + k \,\!$	$f'\left(x\right) = \sqrt {x} \,\!$
$f\left(x\right) = ax + k \,\!$	$f'\left(x\right) = a \,\!$
$f\left(x\right) = \arctan(x) + k \,\!$	$f'\left(x\right) = \frac{1}{1+x^2} \,\!$

domingo, 3 de marzo de 2013