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The given function is:

\[
y = \frac{530}{\sqrt{x}}
\]

To find \( \frac{dy}{dx} \), we will differentiate this function with respect to \(x\).

### Steps to differentiate:
1. Rewrite the function in a more convenient form:
   \[
   y = 530 \cdot x^{-\frac{1}{2}}
   \]
   This makes it easier to apply the power rule.

2. Apply the power rule of differentiation: 
   \[
   \frac{d}{dx} \left( x^n \right) = n \cdot x^{n-1}
   \]
   
   So, differentiating \( y = 530 \cdot x^{-\frac{1}{2}} \):
   \[
   \frac{dy}{dx} = 530 \cdot \left( -\frac{1}{2} \right) \cdot x^{-\frac{3}{2}}
   \]

3. Simplify the result:
   \[
   \frac{dy}{dx} = -\frac{530}{2} \cdot x^{-\frac{3}{2}}
   \]
   or equivalently:
   \[
   \frac{dy}{dx} = -\frac{530}{2\sqrt{x^3}}
   \]

Thus, the derivative is:

\[
\frac{dy}{dx} = -\frac{530}{2\sqrt{x^3}}
\]

Would you like further clarification or additional details?

Here are five related questions you could explore:
1. How does the chain rule apply in more complex differentiation problems?
2. How do you differentiate functions with higher powers of \(x\) under the square root?
3. What is the physical significance of the derivative in real-world applications?
4. Can you explain how to differentiate a function involving multiple variables?
5. How would integration work for a similar function?

**Tip**: When differentiating powers of \(x\), always simplify the function before applying the power rule.

Find dy for the function y = 530 / sqrt(x).

Learn how to differentiate the function y = 530 / sqrt(x). This solution covers the use of the power rule and applies it to find the derivative of y with respect to x. Ideal for students in grades 11-12 or early college calculus.

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