You provided the function:

$f(x) = \frac{6e^{4x} + e^{-15x}}{11e^{4x} + 6e^{-15x}}$

Would you like help simplifying the function, finding its derivative, or performing another analysis on it? Please let me know what you need!

Here are some related questions you might find useful:

1. How would you find the derivative of this function, $f'(x)$?
2. What happens to $f(x)$ as $x \to \infty$ or $x \to -\infty$?
3. Can you rewrite $f(x)$ by factoring terms in the numerator and denominator?
4. How do the exponents in the terms affect the behavior of the function for large or small values of $x$?
5. How can we apply logarithmic differentiation to simplify the process of finding the derivative?

Tip: When simplifying exponential functions, consider factoring out common exponential terms to make the expression more manageable!