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The problem in the image asks for the derivative of the function:

\[
F(x) = \frac{2x^2 - 2x - 7}{2x^3 + x^2 - 2}
\]

### Steps to calculate the derivative:

We will use the **quotient rule** for derivatives, which states:

\[
\frac{d}{dx} \left( \frac{u(x)}{v(x)} \right) = \frac{u'(x) v(x) - u

Calcule la derivada de la siguiente función: F(x) = (2x^2 - 2x - 7) / (2x^3 + x^2 - 2)

Learn how to find the derivative of the function F(x) = (2x^2 - 2x - 7) / (2x^3 + x^2 - 2) using the Quotient Rule. This solution covers calculus concepts and the step-by-step process for applying the quotient rule to rational functions. Suitable for university students in Calculus I or II.

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