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3.8: Tear-Regla del Producto

  • Page ID
    116572
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    1. Tomar las derivadas de las siguientes funciones.
      1. \(f(x) = x^2 e^x\)
        \(f'(x) = x^2 e^x + 2x e^x\)
        ans
      2. \(g(x) = \left(\sqrt{x} + 1\right)\left(x^2\right)\)
        ans
      3. \(h(x) = \frac{1}{x} \left(e^x + 1 \right)\)
        \(h'(x) = -\frac{1}{x^2} (e^x + 1) + \frac{1}{x} e^x\)
        ans
      4. \(i(x) = \ln(x) x\)
        \(i'(x) = 1 + \ln(x)\)
        ans
      5. \(j(x) = \sqrt{x} \ln(x)\)
        \(j(x) = \frac{1}{2 \sqrt{x}} \ln(x) + \frac{1}{\sqrt{x}}\)
        ans
      6. \(m(x) = (x^3 + x^2) \sin(x)\)
        \(m'(x) = (3x^2 + 2x) \sin(x) + (x^3 + x^2) \cos(x)\)
        ans
      7. \(l(x) = e^{2x}\)(Pista: Puedes reescribir esto como\(e^x \cdot e^x\))
        \(l'(x) = 2 e^{2x}\)
        ans
      8. \(\ell(x) = x e^x \ln(x)\)
        \(\ell'(x) = e^x \ln(x) + e^x \ln(x) + e^x\)
        ans

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