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tabla de derivadas
Regla de la cadena d dx. {f(g[h(
x
)])} = f (g[h(
x
)])g [h(
x
)]h (
x
) d dx. (xk) = kxk−1 d dx. [f(
x
)k] = kf(
x
)k−1f (
x
). Potencia d dx. (. √
x
) = d dx. (x1/2) = 1. 2. √
x
d dx. [. √.
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Informe
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
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