C´
ALCULO DE DERIVADAS
d
dx (C) = 0, para todo C∈R(La derivada de una constantes es siempre 0)
d
dx [xn] = n xn−1, si n6= 0 d
dx [f(x)n] = f(x)n−1·f0(x), si n6= 0
d
dx [ln x] = 1
x
d
dx [ln f(x)] = 1
f(x)·f0(x)
d
dx [ex] = exd
dx hef(x)i=ef(x)·f0(x)
d
dx [ax] = ax·ln ad
dx haf(x)i=af(x)·ln a·f0(x)
d
dx [sen x] = cos xd
dx [sen (f(x))] = cos (f(x)) ·f0(x)
d
dx [cos x] = −sen xd
dx [cos (f(x))] = −sen (f(x)) ·f0(x)
d
dx [tan x] = 1
cos2x
d
dx [tan (f(x))] = 1
cos2(f(x)) ·f0(x)
d
dx [cotan x] = −1
sen2x
d
dx [cotan (f(x))] = −1
sen2(f(x)) ·f0(x)
d
dx [arc sen x] = 1
√1−x2
d
dx [arc sen (f(x))] dx =1
p1−f(x)2·f0(x)
d
dx [arc cos x] = −1
√1−x2
d
dx [arc cos (f(x))] dx =−1
p1−f(x)2·f0(x)
d
dx [arctan x] = 1
1 + x2
d
dx [arctan (f(x))] = 1
1 + f(x)2·f0(x)
0Dpto. Matem´atica Aplicada I, Universidad de Sevilla
