The function you're asking for is \( f(x) = \sqrt[3]{x^4} \), which can be rewritten as \( f(x) = (x^4)^{1/3} = x^{4/3} \).

Now, let's differentiate \( f(x) = x^{4/3} \) with respect to \( x \).

### Derivative:
\[
\frac{d}{dx} \left( x^{4/3} \right) = \frac{4}{3}x^{\frac{4}{3} - 1} = \frac{4}{3}x^{1/3}
\]

So, the derivative of \( \sqrt[3]{x^4} \) is:
\[
\frac{d}{dx} \left( \sqrt[3]{x^4} \right) = \frac{4}{3}x^{1/3}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the derivative of any power function?
2. What is the chain rule, and how does it apply to functions with roots?
3. How do we interpret fractional exponents geometrically?
4. Can you differentiate other root functions like \( \sqrt{x} \)?
5. How do higher-order derivatives behave for root functions?

**Tip:** Always express roots as fractional exponents for easier differentiation.

Discover how to differentiate the cube root of x^4 with a detailed solution. Learn about the power rule, fractional exponents, and the step-by-step process to find the derivative of this function. This tutorial is ideal for high school students in Grades 11-12.

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