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The question is asking for an antiderivative (or indefinite integral) of the function \( f(x) = \frac{1}{\sqrt{x}} \).

Let's solve it step-by-step:

1. Rewrite \( f(x) \) in a more convenient form:
   \[
   f(x) = \frac{1}{\sqrt{x}} = x^{-\frac{1}{2}}
   \]

2. To find an antiderivative, we integrate \( f(x) \):
   \[
   \int x^{-\frac{1}{2}} \, dx
   \]

3. Apply the power rule for integration:
   \[
   \int x^{-\frac{1}{2}} \, dx = \frac{x^{-\frac{1}{2} + 1}}{-\frac{1}{2} + 1} = \frac{x^{\frac{1}{2}}}{\frac{1}{2}} = 2x^{\frac{1}{2}} = 2\sqrt{x}
   \]

Thus, the antiderivative of \( f(x) = \frac{1}{\sqrt{x}} \) is \( 2\sqrt{x} \).

### Answer:
The correct option is:
- \( 2\sqrt{x} \)

Would you like more details or have any questions about this solution?

### Related Questions:
1. What are the general rules for finding antiderivatives of functions?
2. How does the power rule apply to integration?
3. Why do we add a constant \( C \) to indefinite integrals?
4. How would you find the antiderivative of \( f(x) = x^{n} \) for any \( n \)?
5. What is the difference between definite and indefinite integrals?

**Tip:** Always remember to check if the integral requires a constant of integration \( C \) when calculating indefinite integrals.

Una primitiva de f(x) = 1 / sqrt(x) es: Seleccione una: ln(sqrt(x)), -(1/2)x^(-3/2), La respuesta correcta no aparece, sqrt(x), 2sqrt(x)

Learn how to find the antiderivative of f(x) = 1 / sqrt(x) with a step-by-step solution. This calculus problem covers the use of the power rule for integration and is suitable for students in Grades 11-12.

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