Aplica la regla del producto para calcular las derivadas de las siguientes funciones : a. F(x) = x ^ 6 . Sen x b. F(x) = x ^ 2 . √x c. F(x) = x ^ 2 . Lnx d. F(x) = (x ^ 3 - 2x) . E ^ x e. F(x) = ln x. Cosx Ayúdenme es para una tarea.
En resumen
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Se determinan la derivada de cada función haciendo uso de la regla del productoLa regla del producto dice que la derivada del producto de dos funciones f(x) y g(x) es : (f(x) * g(x))' = f'(x) * g(x) + g'(x) * f(x)Calculemos las derivadasa.
F(x) = x⁶.
Sen x : f'(x) = 6x⁵ * sen(x) + cos(x) * x⁶ = x⁵ * (6sen(x) + xcos(x))b.
F(x) = x² * √x : f'(x) = 2x * √x + 1 / (2√x
) * x² = 2x * √x + 0.
5x * √x = 2.
5x * √xc.
F(x) = x² .
Lnx : f'(x) = 2x * ln(x) + (1 / x) * x² = 2xln(x) + x = x * (2ln(x) + 1)d.
F(x) = (x³ - 2x) .
Eˣ : f'(x) (3x² - 2) * eˣ + eˣ * (x³ - 2x) = eˣ * (x³ + 3x² - 2x - 2)e.
F(x) = ln x.
Cosxf'(x) = (1 / x) * cos(x) - sen(x) * ln(x) Puedes visitar : brainly.
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