# Problem of the Week

## Updated at Feb 3, 2014 2:01 PM

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

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

Here are the steps:

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

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