# Problem of the Week

## Updated at Apr 16, 2018 10:34 AM

To get more practice in calculus, we brought you this problem of the week:

How would you differentiate $$8x\sin{x}$$?

Check out the solution below!

$\frac{d}{dx} 8x\sin{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$8(\frac{d}{dx} x\sin{x})$2 Use Product Rule to find the derivative of $$x\sin{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$8((\frac{d}{dx} x)\sin{x}+x(\frac{d}{dx} \sin{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$8(\sin{x}+x(\frac{d}{dx} \sin{x}))$4 Use Trigonometric Differentiation: the derivative of $$\sin{x}$$ is $$\cos{x}$$.$8(\sin{x}+x\cos{x})$Done8*(sin(x)+x*cos(x))