Calcula la derivada de las siguientes funciones usando la regla del producto: $(f \cdot g)' = f' \cdot g + f \cdot g'$
Ejercicio 1
\[f(x) = x \cdot e^x\]
\[f'(x) = \mathbf{?}\]
\[f'(x) = \mathbf{?}\]
Ejercicio 2
\[f(x) = 2x \cdot e^x\]
\[f'(x) = \mathbf{?}\]
\[f'(x) = \mathbf{?}\]
Ejercicio 3
\[f(x) = x^2 \cdot e^x\]
\[f'(x) = \mathbf{?}\]
\[f'(x) = \mathbf{?}\]
Ejercicio 4
\[f(x) = e^x \cdot \sin(x)\]
\[f'(x) = \mathbf{?}\]
\[f'(x) = \mathbf{?}\]
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