Question

Find the derivative of $e^{3lo{g}_{e}x}$ with respect to x.

Answer 1

her, we are given $y=e^{3\log e^x}$.

So, $y=e^{\log e^{x^3}}$

From the exponent & logarithmic properties. $y=a^{\log a^b}=b$.

So, $y=x^3$

now, $\frac{dy}{dx}=3x^2$

or $\frac{dy}{dx}=3e^{\log e^{x^e}}$

$\frac{dy}{dx}=3e^{2\log e^x}$.