Tabla de Derivadas Usuales

F(x)

F'(x)

K

0

mx+b

m

(k f(x))

k f'(x)

x^m

_mX^m-1

In X

1/X

In g(x)

g'(x) / g(x)

[f(x) + g(x)]'

f'(x) + g'(x)

[f(x) - g(x)]'

f'(x) - g'(x)

(f . g)' (x)

f'(x) g(x) + f(x) g'(x)

[ f(x) ] '�

g(x)

f'(x) g(x) - f(x) g'(x)

[g(x)']�

sen x

cos x

cos x

- sen x

(tg x)'

1 + tg²x = sec²x = 1 / cos²x

(cotg x)'

-(1 + cotg²x) = -cosec² x =

-1/sen²x

(sec x)'

sec x . tg x

(cosec x)'

-cosec x . cotg x

e^x

e^x

k^x

k^x .In k

k ^g(x)

k ^g(x). In k . g' (x)

log _a x

1/x . log _a e

log _a g(x)

1/g(x) . g'(x) log _a e

[g(x)] ^h(x)

[g(x)] ^h(x) [h'(x). In [g(x)] +

h(x) . g'(x)

g(x) ]

g(x)] ^g(x)

g(x)] ^g(x) [1 + In g(x) ] . g'(x)