We are given the function:

$y = \frac{x^4 + 7}{x^2}$

To simplify this, divide each term in the numerator by $x^2$:

$y = \frac{x^4}{x^2} + \frac{7}{x^2}$

Simplifying each term:

$y = x^{4-2} + 7x^{-2}$

$y = x^2 + 7x^{-2}$

Now that the function is simplified, we can proceed to find the derivative.

Would you like to continue with finding the derivative?

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Follow-up questions:

1. What are the rules for simplifying fractions involving exponents?
2. How does dividing a polynomial by a monomial simplify a function?
3. What is the power rule for derivatives, and how does it apply here?
4. How would you approach finding the derivative of a more complex function?
5. What are some real-world applications of derivatives?

Tip: Simplifying functions before differentiation can make finding derivatives much easier.