# Problem of the Week

## Updated at Mar 24, 2014 9:26 AM

For this week we've brought you this calculus problem.

How can we solve for the derivative of $$\ln{x}{e}^{x}$$?

Here are the steps:

$\frac{d}{dx} \ln{x}{e}^{x}$

 1 Use Product Rule to find the derivative of $$\ln{x}{e}^{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} \ln{x}){e}^{x}+\ln{x}(\frac{d}{dx} {e}^{x})$2 The derivative of $$\ln{x}$$ is $$\frac{1}{x}$$.$\frac{{e}^{x}}{x}+\ln{x}(\frac{d}{dx} {e}^{x})$3 The derivative of $${e}^{x}$$ is $${e}^{x}$$.$\frac{{e}^{x}}{x}+\ln{x}{e}^{x}$Donee^x/x+ln(x)*e^x