displaystyled/dx≤ft(e^2log_e x^3) equals

The correct answer is Option (2) → \(6x^5\)

Since \(m\log_e a = \log_e a^m\) and \(e^{\log_e a} = a\), the function simplifies:

    \(2\log_e x^3 = \log_e (x^3)^2 = \log_e x^6\)
    \(e^{2\log_e x^3} = e^{\log_e x^6} = x^6\)

So

    \( \displaystyle \frac{d}{dx}\left(x^6\right) = 6x^5 \)