Tabla de Derivadas

Derivadas y Operaciones con Funciones

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

(f . g)(x) (f . g)(x) = f'(x) . g(x) + f(x) . g'(x)

(f / g)(x) (f / g)(x) = [ f'(x) . g(x) - f(x) . g'(x)] / g2(x)

(g o f)(x) (g 0 f)'(x) = g'(fx) . f'(x)

k f(x) (k.f)'(x) = k . f'(x)

Derivadas de Funciones

f(x) = cte.

f'(x) = 0

f(x) = x

f'(x) = 1

f(x) = x2

f'(x) = 2x

f(x) = xn

f'(x) = n . xn-1 x>0

f(x) = U(x)n

f'(x) = n . U(x)n-1 . U'(x)

f(x) = 1 / x

f'(x) = - 1 / x2

f(x) = 1 / U

f'(x) = - U' / U2

f(x) = ex

f'(x) = ex

f(x) = eU(x)

f'(x) = U' . eU

f(x) = ln x Df=R+

f'(x) = 1 / x

f(x) = ln U(x)

f'(x) = U' / U

f(x) = "(x)

f'(x) = 1 / 2"x

f(x) = "[U(x)]

f'(x) = U' / 2"(U)

f(x) = sen(x)

f'(x) = cos(x)

f(x) = sen U

f'(x) = U' . cosU

f(x) = cos(x)

f'(x) = - sen(x)

f(x) = cos U

f'(x) = - U' . senU

f(x) = tg(x)

f'(x) = 1 / cos2(x)

f(x) = tg U

f'(x) = U' / cos2U

f(x) = sec(x)

f'(x) = senx / cos2x

f(x) = sec U

f'(x) = (U' . senU) / cos2U

f(x) = cosec(x)

f'(x) = - cosx / sen2x

f(x) = cosec U

f'(x) = - (U' . cosU) / sen2U

f(x) = cotg(x)

f'(x) = - 1 / sen2(x)

f(x) = cotg U

f'(x) = - U' / sen2U

f(x) = arcsen(x)

f'(x) = 1 / "(1 - x2)

f(x)= arcsen U

f'(x) = U' / "(1 - U2)

f(x) = arccos(x)

f'(x) = - 1 / "(1 - x2)

f(x) = arcos U

f'(x) = U' / "(1 - U2)

f(x) = arctg(x)

f'(x) = 1 / (1 + x2)

f(x) = arctg U

f'(x) = U' / (1 + U2)