What is the derivative of f(x)=(e^(2x))(ln(x))?

Mar 3, 2017

$f ' \left(x\right) = {e}^{2 x} \left(2 \ln x + \frac{1}{x}\right)$

Explanation:

The derivative of $\ln x$ is $\frac{1}{x}$
The derivative of ${e}^{g} \left(x\right)$is ${e}^{g} \left(x\right) \cdot g ' \left(x\right)$
The derivative of $h \left(x\right) \cdot l \left(x\right)$ is $h ' \left(x\right) \cdot l \left(x\right) + h \left(x\right) \cdot l ' \left(x\right)$

Then

$f ' \left(x\right) = {e}^{2 x} \cdot 2 \cdot \ln x + {e}^{2 x} \cdot \frac{1}{x}$

$= {e}^{2 x} \left(2 \ln x + \frac{1}{x}\right)$