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The given expression to differentiate is:

\[
y = \frac{x^6 - 2}{x^3}
\]

### Step 1: Simplify the expression
We can simplify the expression before differentiating:

\[
y = \frac{x^6}{x^3} - \frac{2}{x^3}
\]

Simplifying further:

\[
y = x^{6-3} - 2x^{-3}
\]

\[
y = x^3 - 2x^{-3}
\]

### Step 2: Differentiate with respect to \(x\)

The derivative of \(y\) with respect to \(x\) is:

\[
\frac{dy}{dx} = \frac{d}{dx}(x^3) - \frac{d}{dx}(2x^{-3})
\]

For \(x^3\):

\[
\frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2
\]

For \(-2x^{-3}\):

\[
\frac{d}{dx}(2x^{-3}) = 2 \cdot (-3) x^{-3-1} = -6x^{-4}
\]

### Final Result:
Thus, the derivative is:

\[
\frac{dy}{dx} = 3x^2 + 6x^{-4}
\]

Or equivalently:

\[
\frac{dy}{dx} = 3x^2 + \frac{6}{x^4}
\]

Would you like more details or have any questions? 

Here are five related questions you could explore:
1. What is the derivative of \( y = \frac{3x^5 - 7}{x^2} \)?
2. How do you find the second derivative of \( y = x^3 - 2x^{-3} \)?
3. What is the physical interpretation of the derivative in calculus?
4. Can you differentiate \( y = x^4 + \frac{1}{x^2} \) using the power rule?
5. How do you apply the chain rule in differentiation?

**Tip:** Simplifying the expression before differentiating often makes the process easier and reduces the chance of errors.

Explore how to differentiate y = (x^6 - 2) / x^3 by simplifying the expression first and then applying the Power Rule. This detailed step-by-step solution is suitable for students in Grades 11-12.

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