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3.10: Tartaria- Regla del cociente

  • Page ID
    116571
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    1. Encuentra las derivadas de las siguientes funciones.
      1. \(f(x) = \frac{e^x}{x}\)
        \(f'(x) = \frac{x e^x - e^x}{x^2}\)
        ans
      2. \(g(x) = \frac{\sqrt[3]{x}}{\ln(x)}\)
        ans
      3. \(h(x) = \frac{1}{x^2 + 5x + 6}\)
        \(h'(x) = \frac{-(2x + 5)}{(x^2 + 5x + 6)^2}\)
        ans
      4. \(i(x) = \frac{\cos(x)}{1 + x^2}\)
        \(i'(x) = \frac{-(1 + x^2) \sin(x) - 2x \cos(x)}{(1 + x^2)^2}\)
        ans
      5. \(j(x) = \frac{\ln(x)}{x^2}\)
        \(j'(x) = \frac{1 - 2 \ln(x) }{x^3}\)
        ans
      6. \(k(x) = e^{-x}\)(¿Cómo puedes escribir esto como una fracción?)
        \(k'(x) = \frac{-e^x}{(e^x)^2} = -\frac{1}{e^x}\)
        ans
      7. \(\ell(x) = \frac{x e^x}{1 + x}\)
        \(\ell'(x) = \frac{x^2 e^x + x e^x + e^x}{(1+x)^2}\)
        ans

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