# Problem of the Week

## Updated at Jul 31, 2017 11:10 AM

This week's problem comes from the calculus category.

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

Let's begin!

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

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