Tabla de Derivadas Derivadas y Operaciones con Funciones
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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) 1
