Tabla de derivadas y primitivas

(Diferencias entre revisiones)

Revisión de 16:34 30 ago 2011

Suma de funciones: $\frac{\mathrm{d}\ }{\mathrm{d}x}(u+v) = \frac{\mathrm{d}u}{\mathrm{d}x} + \frac{\mathrm{d}v}{\mathrm{d}x}$

Producto de funciones: $\frac{\mathrm{d}\ }{\mathrm{d}x}(uv) = \left(\frac{\mathrm{d}u}{\mathrm{d}x}\right)v + u\left(\frac{\mathrm{d}v}{\mathrm{d}x}\right)$

Caso particular $u = C = cte$

$\frac{\mathrm{d}\ }{\mathrm{d}x}(Cv) = C\left(\frac{\mathrm{d}v}{\mathrm{d}x}\right)$

$\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{\mathrm{d}u}{\mathrm{d}y}\,\frac{\mathrm{d}y}{\mathrm{d}x}$

Caso particular de derivada logarítmica

$\frac{\mathrm{d}\ }{\mathrm{d}x}(\ln(u)) = \frac{1}{u}\,\frac{\mathrm{d}u}{\mathrm{d}x}$

Caso particular de exponencial de una función

$\frac{\mathrm{d}\ }{\mathrm{d}x}\left(\mathrm{e}^u\right) = \mathrm{e}^u\,\frac{\mathrm{d}u}{\mathrm{d}x}$

$f (x)$	$d f / d x$	$f (x)$	$d f / d x$
$C\,$	$0\,$	$\ln(x)\,$	$\frac{1}{x}$
$x\,$	$1\,$	$\mathrm{sen}(x)\,$	$\cos(x)\,$
$x^2\,$	$2x\,$	$\cos(x)\,$	$-\mathrm{sen}(x)\,$
$\frac{1}{x}$	$-\frac{1}{x^2}$	$\mathrm{tg}(x)\,$	$\frac{1}{\cos^2(x)}$
$x^n\,$	$nx^{n-1}\,$	$\mathrm{arcsen}(x)\,$	$\displaystyle\frac{1}{\sqrt{1-x^2}}$
$\mathrm{e}^x\,$	$\mathrm{e}^x\,$	$\mathrm{arccos}(x)\,$	$\displaystyle -\frac{1}{\sqrt{1-x^2}}$
$\mathrm{a}^x\,$	$\ln(a)\,\mathrm{a}^x$	$\mathrm{arctg}(x)\,$	$\displaystyle\frac{1}{1+x^2}$

@@ Línea 8: / Línea 8: @@
 Caso particular <math>u = C = \mathrm{cte}</math>
-:<math>\frac{\mathrm{d}\ }{\mathrm{d}x}(Cv) = C\left(\frac{\mathrm{d}v}{\mathrm{d}x})</math>
+:<math>\frac{\mathrm{d}\ }{\mathrm{d}x}(Cv) = C\left(\frac{\mathrm{d}v}{\mathrm{d}x}\right)</math>
 ;Regla de la cadena