4. Sendo $$ f(x)=\frac{x^{3}-1}{2 x} $$ calcule $$ f^{\prime}(-1) $$

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Para calcular a derivada $$ f^{\prime}(x) $$ da função $$ f(x) = \frac{x^{3} - 1}{2x} $$ e determinar $$ f^{\prime}(-1) $$, siga os passos abaixo:

1. **Simplifique a função:**

$$
   f(x) = \frac{x^{3} - 1}{2x} = \frac{x^{3}}{2x} - \frac{1}{2x} = \frac{x^{2}}{2} - \frac{1}{2x}
   $$

2. **Calcule a derivada $$ f^{\prime}(x) $$:**

$$
   f^{\prime}(x) = \frac{d}{dx}\left(\frac{x^{2}}{2}\right) - \frac{d}{dx}\left(\frac{1}{2x}\right) = x - \left(-\frac{1}{2x^{2}}\right) = x + \frac{1}{2x^{2}}
   $$

3. **Avalie a derivada em $$ x = -1 $$:**

$$
   f^{\prime}(-1) = (-1) + \frac{1}{2(-1)^{2}} = -1 + \frac{1}{2} = -\frac{1}{2}
   $$

Portanto, o valor da derivada em $$ x = -1 $$ é:

$$
f^{\prime}(-1) = -\frac{1}{2}
$$
$$ f^{\prime}(-1) = -\frac{1}{2} $$

4. Sendo \( f(x)=\frac{x^{3}-1}{2 x} \) calcule \( f^{\prime}(-1) \)

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