To find the derivative of \( f(x) = \sqrt{x} \), we can first rewrite \( \sqrt{x} \) as a power of \( x \):

\[
f(x) = x^{\frac{1}{2}}
\]

Now, apply the power rule for derivatives, which states that if \( f(x) = x^n \), then \( f'(x) = n \cdot x^{n-1} \).

In our case:

\[
f'(x) = \frac{1}{2} \cdot x^{\frac{1}{2} - 1} = \frac{1}{2} \cdot x^{-\frac{1}{2}}
\]

This can be rewritten as:

\[
f'(x) = \frac{1}{2\sqrt{x}}
\]

Thus, the derivative of \( f(x) = \sqrt{x} \) is:

\[
f'(x) = \frac{1}{2\sqrt{x}}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What is the derivative of \( f(x) = \sqrt{2x} \)?
2. How would you find the second derivative of \( f(x) = \sqrt{x} \)?
3. What is the derivative of \( f(x) = \frac{1}{\sqrt{x}} \)?
4. Can you compute the derivative of \( f(x) = x^{3/2} \)?
5. What is the derivative of \( f(x) = x^{1/3} \)?

**Tip**: When differentiating square roots, always try to rewrite the expression as a power for easier application of derivative rules.

Find the derivative of f(x) = sqrt(x) using the power rule for derivatives. Learn how to apply this rule to solve calculus problems, and explore related practice questions. Suitable for students in Grades 11-12 or Calculus 1.

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