Tabla de Derivadas Derivadas y Operaciones con Funciones

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)
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