# Problem of the Week

## Updated at Nov 17, 2014 8:42 AM

How can we find the derivative of $$x\sin{x}$$?

Below is the solution.

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

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