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The question asks you to determine the derivative of the function \( f(x) = \sqrt{\frac{7}{x}} \), starting by expressing the function as a composition of two functions \( u(x) \) and \( v(x) \), so that \( f(x) = u(v(x)) \).

Given that \( v(x) = \frac{7}{x} \), the next step is to express \( u(x) \), which will involve taking the square root.

Since the original function is \( f(x) = \sqrt{v(x)} \), we can define:
\[
u(x) = \sqrt{x}
\]

Now, we have:
\[
f(x) = u(v(x)) = \sqrt{\frac{7}{x}}
\]

Would you like to proceed with finding the derivative using the chain rule, or do you have any specific questions about this part?

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### Related Questions:
1. How is the chain rule used to differentiate composite functions?
2. How can \( v(x) = \frac{7}{x} \) be differentiated with respect to \( x \)?
3. What is the derivative of \( u(x) = \sqrt{x} \)?
4. Can we simplify \( f(x) = \sqrt{\frac{7}{x}} \) before applying the derivative?
5. How does the derivative of square root functions behave in general?

### Tip:
When applying the chain rule, always break the function down into simpler components and differentiate each part step by step.

Bestimme die Ableitung der Funktion f(x) = √(7/x). Schreibe die Funktion als Verkettung von u(x) und v(x) so dass f(x) = u(v(x)).

This problem demonstrates how to differentiate the function f(x) = √(7/x) by expressing it as a composition of two functions u(x) and v(x). The solution includes applying the chain rule and simplifying the result. Suitable for Grades 11-12.

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