Matematicas

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Ejercicios de derivadas e integrales

Este material puede descargarse desde http://www.uv.es/~montes/biologia/matcero.pdf

Departament d’Estad´ıstica i Investigaci´o Operativa
Universitat de Val`encia

Derivadas

Reglas de derivacion

| ||
| |d [f (x) + g(x)] = f 0 (x) + g0 (x) |
|Suma |dx |
| | |
| |d [kf (x)] =kf 0 (x) |
| |dx |
|Producto | |
| |d [f (x)g(x)] = f 0 (x)g(x) + f (x)g0 (x)|
| |dx |
| |d · f (x) ¸ = f 0 (x)g(x) − f (x)g0 (x) |
| |dx g(x) g(x)2 |
|Cociente| |
| | |
| |d |
| |dx {f [g(x)]} = f 0 [g(x)]g0 (x)|
|Regla de la cadena | |
| |d |
| |dx {f (g[h(x)])} = f 0 (g[h(x)])g0 [h(x)]h0 (x) |
|| |
| |d (xk ) = kxk−1 d [f (x)k ] = kf (x)k−1 f 0 (x) |
| |dx dx |
| ||
| |d (√x) = d (x1/2 ) = 1 d [pf (x)] = f 0 (x) |
|Potencia |dx dx 2√x dx 2pf (x) |
| |d µ 1 ¶ d 1 d · 1 ¸ f 0 (x)|
| |= (x−1 ) = − = − |
| |dx x dx x2 dx f (x) f (x)2 |

Reglas de derivacion (continuacion)

| ||
| |d (sin x) = cos x d [sin f (x)] = cos f (x)f 0 (x) |
| |dx dx |
| | |
|...