What is $\frac{d}{dx}\left(e^{3\log x}\right)$ for $x > 0$?

Explanation

1. 01

   $e^{3\log x} = e^{\log x^{3}} = x^{3}$ for $x > 0$.

2. 02

   So the derivative is $3x^{2}$; the chain rule gives the same, $e^{3\log x} \cdot \frac{3}{x} = x^{3} \cdot \frac{3}{x}$.