Derivadas Reglas de derivaci´ on

Suma

Producto

d [f (x) + g(x)] = f 0 (x) + g 0 (x) dx d [kf (x)] = kf 0 (x) dx d [f (x)g(x)] = f 0 (x)g(x) + f (x)g 0 (x) dx

Cociente

Regla de la cadena

· ¸ d f (x) f 0 (x)g(x) − f (x)g 0 (x) = dx g(x) g(x)2 d {f [g(x)]} = f 0 [g(x)]g 0 (x) dx d {f (g[h(x)])} = f 0 (g[h(x)])g 0 [h(x)]h0 (x) dx

Potencia

d k (x ) = kxk−1 dx

d [f (x)k ] = kf (x)k−1 f 0 (x) dx

d √ d 1/2 1 ( x) = (x ) = √ dx dx 2 x

d p f 0 (x) [ f (x)] = p dx 2 f (x)

d dx

µ ¶ 1 d −1 1 = (x ) = − 2 x dx x

· ¸ d 1 f 0 (x) =− dx f (x) f (x)2

2

Reglas de derivaci´ on (continuaci´ on)

Trigonom´ etricas

Funciones de arco

Exponenciales

d (sin x) = cos x dx

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

d (cos x) = − sin x dx

d [cos f (x)] = − sin f (x)f 0 (x) dx

d (tan x) = 1 + tan2 x dx

d [tan f (x)] = [1 + tan2 f (x)]f 0 (x) dx

d 1 (arcsin x) = √ dx 1 − x2

d f 0 (x) [arcsin f (x)] = p dx 1 − f (x)2

d −1 (arc cos x) = √ dx 1 − x2

d −f 0 (x) [arc cos f (x)] = p dx 1 − f (x)2

d 1 (arctan x) = dx 1 + x2

d f 0 (x) [arctan f (x)] = dx 1 + f (x)2

d x (e ) = ex dx

d f (x) (e ) = ef (x) f 0 (x) dx

d x (a ) = ax ln a dx

d f (x) (a ) = af (x) ln af 0 (x) dx

d 1 (ln x) = dx x

d f 0 (x) (ln f (x)) = dx f (x)

d 1 1 (lg x) = dx a x ln a

d f 0 (x) 1 (lga f (x)) = dx f (x) ln a

Logar´ıtmicas