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To solve for the derivative of the given function \( f(x) = x^{\frac{4}{3}} \), we can apply the power rule, which states:

\[
\frac{d}{dx} \left( x^n \right) = n \cdot x^{n-1}
\]

Here, \( n = \frac{4}{3} \).

Using the power rule:

\[
f'(x) = \frac{4}{3} \cdot x^{\frac{4}{3} - 1} = \frac{4}{3} \cdot x^{\frac{1}{3}}
\]

Thus, the derivative is:

\[
f'(x) = \frac{4}{3} \cdot x^{\frac{1}{3}}
\]

Would you like more details or have any questions? Here are some related questions:

1. How does the power rule apply to negative exponents?
2. What happens if the exponent is a fraction, like in this case?
3. How do we differentiate functions involving products or quotients?
4. How would you integrate \( x^{\frac{4}{3}} \)?
5. Can we apply this method to logarithmic or exponential functions?

**Tip**: Always simplify the exponent first before applying the power rule to ensure accuracy.

Look for the most convenient way to find the derivative of f(x) = x^(4/3).

Find the derivative of the function f(x) = x^(4/3) using the power rule. This detailed solution applies the fundamental differentiation formula to calculate the derivative for this algebraic expression. Suitable for students in Grades 11-12 or early college level.

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