The function you have provided is:

$f(x) = \left( \sqrt[3]{\sin^2(x)} \right)^{\arctan(x)}$

To break it down:

• The inside function is $\sin^2(x)$, which is the sine of $x$ squared.
• This is then taken to the cube root, indicated by $\sqrt[3]{ }$.
• The entire result is then raised to the power of $\arctan(x)$, the arctangent of $x$.

Would you like to:

• Differentiate this function with respect to $x$?
• Evaluate it at a specific point?
• Simplify it further or rewrite in a different form?

Let me know how you'd like to proceed!

Here are five follow-up questions based on this:

1. Would you like to find the derivative of $f(x)$?
2. Would you like to compute the value of $f(x)$ for a specific $x$?
3. Should we explore the limits of $f(x)$ as $x \to 0$ or $x \to \infty$?
4. Would you like to rewrite the function in a different mathematical form?
5. Should we examine how the graph of $f(x)$ behaves?

Tip: When taking derivatives of composite functions like this, use both the chain rule and power rule systematically to simplify the process.