# Problem of the Week

## Updated at Feb 24, 2014 5:25 PM

This week's problem comes from the calculus category.

How would you differentiate $$x\ln{x}$$?

Let's begin!

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

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